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1999-12-11 03:00:00
2025-04-28 00:58:08
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A381425
Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of (1 + x/(1-x)^k)^k.
[ "1", "1", "0", "1", "1", "0", "1", "2", "1", "0", "1", "3", "5", "1", "0", "1", "4", "12", "10", "1", "0", "1", "5", "22", "37", "18", "1", "0", "1", "6", "35", "92", "102", "30", "1", "0", "1", "7", "51", "185", "345", "258", "47", "1", "0", "1", "8", "70", "326", "880", "1188", "606", "70", "1", "0", "1", "9", "92", "525", "1881", "3851", "3796", "1335", "100", "1", "0", "1", "10", "117", "792", "3563", "10002", "15655", "11364", "2781", "138", "1", "0" ]
[ "nonn", "easy", "tabl" ]
109
0
8
[ "A000007", "A000012", "A000326", "A001477", "A071919", "A096000", "A177787", "A362125", "A381425", "A382859" ]
null
Seiichi Manyama, Apr 07 2025
2025-04-11T12:09:07
oeisdata/seq/A381/A381425.seq
8ba0130287b43de760cd6171481b50ea
A381426
A(n,k) is the sum over all ordered partitions of [n] of k^j for an ordered partition with j inversions; square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "1", "1", "1", "1", "1", "2", "1", "1", "3", "4", "1", "1", "4", "13", "8", "1", "1", "5", "36", "75", "16", "1", "1", "6", "79", "696", "541", "32", "1", "1", "7", "148", "3851", "27808", "4683", "64", "1", "1", "8", "249", "14808", "567733", "2257888", "47293", "128", "1", "1", "9", "388", "44643", "5942608", "251790113", "369572160", "545835", "256", "1", "1", "10", "571", "113480", "40065301", "9546508128", "335313799327", "121459776768", "7087261", "512" ]
[ "nonn", "tabl", "changed" ]
23
0
6
[ "A000670", "A011782", "A289545", "A347841", "A347842", "A347843", "A347844", "A347845", "A347846", "A381299", "A381369", "A381426", "A381427" ]
null
Alois P. Heinz, Feb 23 2025
2025-04-19T03:52:59
oeisdata/seq/A381/A381426.seq
0d608cf1e6bbe696b3ca3f3e579e6d42
A381427
Sum over all ordered partitions of [n] of n^j for an ordered partition with j inversions.
[ "1", "1", "4", "79", "14808", "40065301", "2099255895008", "2651651342949844915", "96254339565438079064819328", "116387990444553949414146511586296381", "5327195120249449992420082364255283659438679552", "10333056290045508772052838892223597279253890797441054043823" ]
[ "nonn" ]
14
0
3
[ "A062173", "A135528", "A381299", "A381373", "A381426", "A381427" ]
null
Alois P. Heinz, Feb 23 2025
2025-02-23T17:34:42
oeisdata/seq/A381/A381427.seq
b686ec3f8163766e6b7a27af3b4270af
A381428
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x) * A(x)^2 ).
[ "1", "1", "6", "73", "1344", "33481", "1054656", "40223233", "1802385024", "92827015921", "5403527705856", "350854589607193", "25142008355656704", "1971003462240791161", "167802783944207917056", "15417877986778302551953", "1520661128893781018640384", "160249491538400609431567201", "17969682580669053325124960256" ]
[ "nonn" ]
11
0
3
[ "A006154", "A136630", "A295254", "A381428", "A381429" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T04:19:08
oeisdata/seq/A381/A381428.seq
32b3b1903d9d54e3562fa23ab83384f6
A381429
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x) * A(x)^3 ).
[ "1", "1", "8", "133", "3392", "117601", "5167808", "275334613", "17250670592", "1242994578721", "101273185092608", "9206681997173893", "923928346115182592", "101453787213382443841", "12100018549609932996608", "1557645163271323384461973", "215265839194368088629051392", "31788685348087376561935104961" ]
[ "nonn" ]
8
0
3
[ "A006154", "A136630", "A295254", "A381428", "A381429" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T04:20:19
oeisdata/seq/A381/A381429.seq
e36dadefe446c7445b12e706eec23aeb
A381430
E.g.f. A(x) satisfies A(x) = 1 + sinh(x*A(x)^3).
[ "1", "1", "6", "73", "1368", "34861", "1126368", "44135701", "2034072960", "107823563641", "6463383851520", "432331180935457", "31924171503581184", "2579483385868484005", "226383845487041421312", "21445302563389991287981", "2180974075392495296544768", "237009522316557393020262001", "27409082977094100068471537664" ]
[ "nonn" ]
11
0
3
[ "A136630", "A162653", "A198865", "A381430", "A381443" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T04:21:14
oeisdata/seq/A381/A381430.seq
b1c4d48e1800fd671c3c31e929d6cdb9
A381431
Heinz number of the section-sum partition of the prime indices of n.
[ "1", "2", "3", "4", "5", "5", "7", "8", "9", "7", "11", "10", "13", "11", "11", "16", "17", "15", "19", "14", "13", "13", "23", "20", "25", "17", "27", "22", "29", "13", "31", "32", "17", "19", "17", "25", "37", "23", "19", "28", "41", "17", "43", "26", "33", "29", "47", "40", "49", "35", "23", "34", "53", "45", "19", "44", "29", "31", "59", "26", "61", "37", "39", "64", "23", "19", "67", "38" ]
[ "nonn" ]
10
1
2
[ "A000040", "A000720", "A001222", "A001223", "A003557", "A003963", "A005117", "A047966", "A048767", "A048768", "A050320", "A051903", "A055396", "A056239", "A061395", "A066328", "A089259", "A091602", "A112798", "A116540", "A116861", "A122111", "A130091", "A181819", "A212166", "A217605", "A238745", "A239455", "A270995", "A296119", "A300383", "A317141", "A318360", "A318361", "A351293", "A351294", "A351295", "A380955", "A381078", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381437", "A381438", "A381440", "A381441", "A381452", "A381454" ]
null
Gus Wiseman, Feb 26 2025
2025-02-27T22:58:04
oeisdata/seq/A381/A381431.seq
7c8815fe2c7fe3202243e14cb9682f8b
A381432
Heinz numbers of section-sum partitions. Union of A381431.
[ "1", "2", "3", "4", "5", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "19", "20", "22", "23", "25", "26", "27", "28", "29", "31", "32", "33", "34", "35", "37", "38", "39", "40", "41", "43", "44", "45", "46", "47", "49", "50", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "64", "65", "67", "68", "69", "71", "73", "74", "75", "76", "77", "79", "80", "81", "82", "83" ]
[ "nonn" ]
7
1
2
[ "A000040", "A000720", "A001222", "A001223", "A003557", "A047966", "A048767", "A048768", "A050320", "A051903", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A116861", "A122111", "A130091", "A212166", "A217605", "A238745", "A239455", "A239964", "A270995", "A296119", "A300383", "A317081", "A317141", "A318360", "A318361", "A351293", "A351294", "A351295", "A381078", "A381431", "A381432", "A381433", "A381436", "A381437", "A381440", "A381441", "A381452", "A381454" ]
null
Gus Wiseman, Feb 27 2025
2025-02-28T10:35:51
oeisdata/seq/A381/A381432.seq
0eb441b914978c55f311fe6553b22e73
A381433
Heinz numbers of non section-sum partitions. Complement of A381431.
[ "6", "12", "18", "21", "24", "30", "36", "42", "48", "54", "60", "63", "66", "70", "72", "78", "84", "90", "96", "102", "105", "108", "110", "114", "120", "126", "132", "138", "140", "144", "147", "150", "154", "156", "162", "165", "168", "174", "180", "186", "189", "192", "198", "204", "210", "216", "220", "222", "228", "231", "234", "238", "240", "246", "252", "258" ]
[ "nonn" ]
6
1
1
[ "A000040", "A000720", "A001222", "A001223", "A003557", "A048767", "A048768", "A050320", "A051903", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A116861", "A122111", "A130091", "A181819", "A217605", "A238745", "A239455", "A239964", "A270995", "A296119", "A300383", "A317081", "A317141", "A318360", "A318361", "A351293", "A351294", "A351295", "A381078", "A381431", "A381432", "A381433", "A381436", "A381437", "A381440", "A381441", "A381452", "A381454" ]
null
Gus Wiseman, Feb 27 2025
2025-02-28T10:35:48
oeisdata/seq/A381/A381433.seq
bad3d5dfba2facb599f3511e8ee3dddb
A381434
Numbers appearing only once in A381431 (section-sum partition of prime indices).
[ "1", "2", "3", "4", "8", "9", "10", "14", "15", "16", "20", "22", "27", "28", "32", "33", "35", "40", "44", "45", "50", "55", "56", "64", "75", "77", "80", "81", "88", "98", "99", "100", "112", "128", "130", "135", "160", "170", "175", "176", "182", "190", "195", "196", "200" ]
[ "nonn" ]
14
1
2
[ "A000005", "A000040", "A000720", "A000961", "A001222", "A001223", "A003557", "A048767", "A048768", "A050320", "A051903", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A116861", "A122111", "A130091", "A212166", "A217605", "A239455", "A239964", "A296119", "A300383", "A317081", "A317141", "A318360", "A318361", "A351293", "A351294", "A351295", "A381078", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381437", "A381440", "A381441", "A381452", "A381454", "A381540", "A381541" ]
null
Gus Wiseman, Feb 27 2025
2025-03-02T22:34:48
oeisdata/seq/A381/A381434.seq
c0b46c51adcdeffe294fb3631af38942
A381435
Numbers appearing more then once in A381431 (section-sum partition of prime indices).
[ "5", "7", "11", "13", "17", "19", "23", "25", "26", "29", "31", "34", "37", "38", "39", "41", "43", "46", "47", "49", "51", "52", "53", "57", "58", "59", "61", "62", "65", "67", "68", "69", "71", "73", "74", "76", "79", "82", "83", "85", "86", "87", "89", "91", "92", "93", "94", "95", "97", "101", "103", "104", "106", "107", "109", "111", "113", "115", "116", "117", "118", "119" ]
[ "nonn" ]
13
1
1
[ "A000005", "A000040", "A000720", "A000961", "A001222", "A001223", "A003557", "A048767", "A048768", "A050320", "A051903", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A116861", "A122111", "A130091", "A212166", "A217605", "A239455", "A239964", "A296119", "A300383", "A317081", "A317141", "A318360", "A318361", "A351293", "A351294", "A351295", "A381078", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381437", "A381440", "A381441", "A381452", "A381454", "A381540", "A381541" ]
null
Gus Wiseman, Feb 27 2025
2025-03-02T22:34:33
oeisdata/seq/A381/A381435.seq
10ec3159a7055ad768614963ebe5258d
A381436
Irregular triangle read by rows where row k is the section-sum partition of the prime indices of n.
[ "1", "2", "1", "1", "3", "3", "4", "1", "1", "1", "2", "2", "4", "5", "3", "1", "6", "5", "5", "1", "1", "1", "1", "7", "3", "2", "8", "4", "1", "6", "6", "9", "3", "1", "1", "3", "3", "7", "2", "2", "2", "5", "1", "10", "6", "11", "1", "1", "1", "1", "1", "7", "8", "7", "3", "3", "12", "9", "8", "4", "1", "1", "13", "7", "14", "6", "1", "5", "2", "10", "15", "3", "1", "1", "1", "4", "4", "4", "3", "9", "7", "1", "16", "3", "2", "2" ]
[ "nonn", "tabf" ]
6
1
2
[ "A000005", "A000040", "A000720", "A000961", "A001222", "A003557", "A003963", "A005117", "A047966", "A048767", "A050320", "A051903", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A116861", "A122111", "A130091", "A181819", "A238744", "A238745", "A239455", "A270995", "A296119", "A300383", "A317141", "A318360", "A318361", "A351293", "A351294", "A351295", "A380955", "A381078", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381437", "A381438", "A381440", "A381441", "A381452", "A381454" ]
null
Gus Wiseman, Feb 28 2025
2025-02-28T23:12:09
oeisdata/seq/A381/A381436.seq
876aa593e107d407a29ba6465e8b76e8
A381437
Last part of the section-sum partition of the prime indices of n.
[ "0", "1", "2", "1", "3", "3", "4", "1", "2", "4", "5", "1", "6", "5", "5", "1", "7", "2", "8", "1", "6", "6", "9", "1", "3", "7", "2", "1", "10", "6", "11", "1", "7", "8", "7", "3", "12", "9", "8", "1", "13", "7", "14", "1", "2", "10", "15", "1", "4", "3", "9", "1", "16", "2", "8", "1", "10", "11", "17", "1", "18", "12", "2", "1", "9", "8", "19", "1", "11", "8", "20", "1", "21", "13", "3", "1", "9", "9", "22", "1", "2" ]
[ "nonn" ]
6
1
3
[ "A000040", "A000720", "A001221", "A001222", "A001223", "A003557", "A008578", "A047966", "A048767", "A050320", "A051903", "A051904", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A116861", "A122111", "A130091", "A181819", "A239455", "A270995", "A296119", "A318360", "A318361", "A351293", "A351294", "A351295", "A360013", "A380955", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381437", "A381438", "A381439", "A381440" ]
null
Gus Wiseman, Feb 28 2025
2025-03-02T08:02:07
oeisdata/seq/A381/A381437.seq
b277f0aa7611aa95eb73b0a59d0979d1
A381438
Triangle read by rows where T(n>0,k>0) is the number of integer partitions of n whose section-sum partition ends with k.
[ "1", "1", "1", "1", "0", "2", "2", "1", "0", "2", "3", "1", "0", "0", "3", "4", "1", "2", "0", "0", "4", "7", "2", "1", "0", "0", "0", "5", "9", "4", "1", "2", "0", "0", "0", "6", "13", "4", "4", "1", "0", "0", "0", "0", "8", "18", "6", "3", "2", "3", "0", "0", "0", "0", "10", "26", "9", "5", "2", "2", "0", "0", "0", "0", "0", "12", "32", "12", "8", "4", "2", "4", "0", "0", "0", "0", "0", "15" ]
[ "nonn", "tabl" ]
6
1
6
[ "A000009", "A000041", "A047966", "A047967", "A048767", "A050320", "A051903", "A051904", "A066328", "A089259", "A091602", "A116540", "A116861", "A122111", "A181819", "A212166", "A239455", "A241131", "A270995", "A296119", "A318360", "A318361", "A351293", "A351294", "A351295", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381437", "A381438", "A381440" ]
null
Gus Wiseman, Mar 01 2025
2025-03-02T08:01:57
oeisdata/seq/A381/A381438.seq
ff395d6962a85f0af766bc9858fe8009
A381439
Numbers whose exponent of 2 in their canonical prime factorization is not larger than all the other exponents.
[ "3", "5", "6", "7", "9", "10", "11", "13", "14", "15", "17", "18", "19", "21", "22", "23", "25", "26", "27", "29", "30", "31", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "45", "46", "47", "49", "50", "51", "53", "54", "55", "57", "58", "59", "61", "62", "63", "65", "66", "67", "69", "70", "71", "73", "74", "75", "77", "78", "79", "81", "82", "83", "85", "86", "87", "89" ]
[ "nonn" ]
6
1
1
[ "A000040", "A000720", "A001221", "A001222", "A001223", "A001694", "A003557", "A005117", "A007814", "A051903", "A051904", "A055396", "A056239", "A061395", "A066328", "A112798", "A122111", "A130091", "A181819", "A212166", "A239455", "A241131", "A351293", "A360013", "A360014", "A360015", "A375669", "A380955", "A381431", "A381436", "A381437", "A381438", "A381439", "A381544" ]
null
Gus Wiseman, Mar 02 2025
2025-03-02T16:04:19
oeisdata/seq/A381/A381439.seq
608b0b6c99c46bf160269addff79cbbe
A381440
Irregular triangle read by rows where row k is the Look-and-Say partition of the prime indices of n.
[ "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "tabf" ]
6
1
4
[ "A000040", "A000720", "A001222", "A003557", "A003963", "A047966", "A048767", "A048768", "A050320", "A051903", "A051904", "A055396", "A056239", "A061395", "A066328", "A071178", "A089259", "A091602", "A112798", "A116540", "A116861", "A122111", "A130091", "A181819", "A212166", "A217605", "A238744", "A239455", "A270995", "A296119", "A300383", "A317141", "A318360", "A318361", "A351293", "A351294", "A351295", "A380955", "A381078", "A381431", "A381432", "A381433", "A381436", "A381437", "A381438", "A381440", "A381441", "A381452", "A381454", "A381540", "A381541" ]
null
Gus Wiseman, Feb 28 2025
2025-02-28T23:12:04
oeisdata/seq/A381/A381440.seq
5b7911016b7e4656f66a81fdeeeda71f
A381441
Number of multisets that can be obtained by partitioning the prime indices of n into a set of sets (set system) and taking their sums.
[ "1", "1", "1", "0", "1", "2", "1", "0", "0", "2", "1", "1", "1", "2", "2", "0", "1", "1", "1", "1", "2", "2", "1", "0", "0", "2", "0", "1", "1", "5", "1", "0", "2", "2", "2", "1", "1", "2", "2", "0", "1", "5", "1", "1", "1", "2", "1", "0", "0", "1", "2", "1", "1", "0", "2", "0", "2", "2", "1", "4", "1", "2", "1", "0", "2", "5", "1", "1", "2", "5", "1", "0", "1", "2", "1", "1", "2", "5", "1", "0", "0", "2", "1", "4", "2", "2", "2" ]
[ "nonn" ]
10
1
6
[ "A000009", "A000040", "A000041", "A000688", "A000720", "A001055", "A001222", "A001223", "A002846", "A003963", "A005117", "A045778", "A050320", "A050326", "A050342", "A050361", "A055396", "A056239", "A061395", "A066328", "A112798", "A116539", "A122111", "A213242", "A213385", "A213427", "A265947", "A279785", "A293243", "A293511", "A296120", "A299202", "A300383", "A300385", "A317141", "A317142", "A318361", "A321469", "A381078", "A381441", "A381452", "A381453", "A381454", "A381455", "A381633", "A381634", "A381635", "A381636", "A381637", "A381715", "A381716" ]
null
Gus Wiseman, Mar 06 2025
2025-03-08T12:23:37
oeisdata/seq/A381/A381441.seq
5f00bbd82d93e73c1c065706890c7be7
A381442
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sinh(x))^2 ).
[ "1", "2", "10", "86", "1080", "18042", "377936", "9538622", "281946496", "9557102450", "365548361472", "15576454300134", "731807446707200", "37584596599753322", "2094995668172597248", "125966553940498047182", "8127048592610380578816", "560040497770823162810082", "41054563701320694564061184" ]
[ "nonn" ]
9
0
2
[ "A136630", "A198865", "A381442" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T04:23:46
oeisdata/seq/A381/A381442.seq
c2168ba1dd9d517d37e198254bfd95a8
A381443
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sinh(x))^3 ).
[ "1", "3", "24", "333", "6720", "179523", "5992800", "240498261", "11287790592", "607019415075", "36813049552896", "2486167829854173", "185070328813031424", "15056826823777670883", "1329283990371617820672", "126573877370649849898149", "12930948581449447912243200", "1410875453109072905123881923" ]
[ "nonn" ]
13
0
2
[ "A136630", "A377554", "A381430", "A381443", "A381450" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T08:52:31
oeisdata/seq/A381/A381443.seq
b601525bc709aa853fae408dc7d13d1f
A381444
Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-2*x * cosh(x)) ) )^(1/2).
[ "1", "1", "5", "52", "837", "18276", "504673", "16871632", "662646281", "29912003344", "1526065495101", "86843677613760", "5454045493422925", "374720831464254016", "27958655248431100313", "2251304544037066606336", "194594761915894781438481", "17971382474574151984603392", "1766073848394482007514748533" ]
[ "nonn" ]
9
0
3
[ "A185951", "A381143", "A381444" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T05:36:03
oeisdata/seq/A381/A381444.seq
73e7bb1e10492676c592ddf2cee36716
A381445
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x) * A(x)^2 ).
[ "1", "1", "6", "75", "1392", "34925", "1108080", "42562807", "1920796416", "99628495353", "5840628226560", "381927689957891", "27562916396961792", "2176123474607538469", "186580455503952427008", "17264834430223073672175", "1714909152672462179205120", "182002038900785304200753777", "20553746198157175799599202304" ]
[ "nonn" ]
10
0
3
[ "A185951", "A205571", "A295256", "A381445", "A381446" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T05:37:07
oeisdata/seq/A381/A381445.seq
7600eb86b8652a1178ecd8f24e73cd14
A381446
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x) * A(x)^3 ).
[ "1", "1", "8", "135", "3456", "120245", "5303040", "283559227", "17830210048", "1289406976713", "105435719470080", "9619902621234191", "968905466782150656", "106779534666615500989", "12781543241568143171584", "1651368425166943566943875", "229049483642619517308764160", "33947359023461155854768564497" ]
[ "nonn" ]
10
0
3
[ "A185951", "A205571", "A295256", "A381445", "A381446" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T05:37:57
oeisdata/seq/A381/A381446.seq
2198172a2776fad634e9c90f29ef324d
A381447
E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2 * cosh(x*A(x)^2).
[ "1", "1", "4", "33", "432", "7745", "175680", "4818457", "155138816", "5738752161", "239890406400", "11184338164241", "575437530083328", "32387311520034913", "1979498673768132608", "130566701113312750665", "9244392468538216611840", "699309477932976288024257", "56289911059840766752456704" ]
[ "nonn" ]
10
0
3
[ "A185951", "A381171", "A381447", "A381448" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T05:39:11
oeisdata/seq/A381/A381447.seq
c04f55338578028662da9151f323192b
A381448
E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^3 * cosh(x*A(x)^3).
[ "1", "1", "6", "75", "1464", "39065", "1324080", "54460987", "2635269504", "146681897553", "9233067686400", "648538095601451", "50289434320131072", "4267083467872455529", "393266542856236148736", "39121731305087283953115", "4178124995723585643970560", "476806534212831941528989217", "57905078072597558361906610176" ]
[ "nonn" ]
10
0
3
[ "A185951", "A381171", "A381447", "A381448" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T05:40:16
oeisdata/seq/A381/A381448.seq
b01de798d3c8dbb113bd52182a2db104
A381449
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x * cosh(x))^2 ).
[ "1", "2", "10", "90", "1224", "22450", "517920", "14395514", "468414464", "17474840226", "735559614720", "34491849224602", "1783268816102400", "100786369113730898", "6182264844496971776", "409065938149354422330", "29043282491002728284160", "2202461172795524123296834", "177675452451923238962528256" ]
[ "nonn" ]
10
0
2
[ "A185951", "A381171", "A381447", "A381449", "A381450" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T05:41:16
oeisdata/seq/A381/A381449.seq
4dec183d0f36d465d716bc0ea4371346
A381450
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x * cosh(x))^3 ).
[ "1", "3", "24", "339", "7056", "195855", "6819840", "286105071", "14055420288", "791783681499", "50327779368960", "3563709848656683", "278223968271034368", "23744747385054558759", "2199369837961901789184", "219748696455778150645575", "23559108001707680103628800", "2697737574531326391439989171" ]
[ "nonn" ]
12
0
2
[ "A185951", "A377554", "A381171", "A381443", "A381448", "A381449", "A381450" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-24T08:52:23
oeisdata/seq/A381/A381450.seq
b59a55624280252bb132c58d9259eec0
A381451
Triangle read by rows: T(n,k) is the clique covering number of the Johnson graph J(n, k), n >= 2, 0 < k < n.
[ "1", "1", "1", "1", "2", "1", "1", "3", "3", "1", "1", "4", "6", "4", "1", "1", "5", "9", "9", "5", "1", "1", "6", "12", "14", "12", "6", "1", "1", "7", "16", "25", "25", "16", "7", "1", "1", "8", "20", "40", "46", "40", "20", "8", "1", "1", "9", "25", "56" ]
[ "nonn", "tabl", "hard", "more" ]
25
2
5
[ "A002620", "A381451" ]
null
Søren Fuglede Jørgensen, Feb 24 2025
2025-03-09T16:50:23
oeisdata/seq/A381/A381451.seq
e721ba5cba81e7c8d8b63b0a9fcbd545
A381452
Number of multisets that can be obtained by partitioning the prime indices of n into a set of multisets and taking their sums.
[ "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "3", "1", "2", "2", "2", "1", "3", "1", "3", "2", "2", "1", "4", "1", "2", "2", "3", "1", "5", "1", "3", "2", "2", "2", "4", "1", "2", "2", "5", "1", "5", "1", "3", "3", "2", "1", "5", "1", "3", "2", "3", "1", "5", "2", "5", "2", "2", "1", "7", "1", "2", "3", "4", "2", "5", "1", "3", "2", "5", "1", "6", "1", "2", "3", "3", "2", "5", "1", "6", "2", "2", "1", "8", "2", "2", "2" ]
[ "nonn" ]
11
1
6
[ "A000009", "A000040", "A000041", "A000688", "A000720", "A001055", "A001222", "A001970", "A002846", "A003963", "A045778", "A050320", "A050326", "A050361", "A055396", "A056239", "A061395", "A066328", "A112798", "A122111", "A213385", "A213427", "A261049", "A265947", "A293243", "A296118", "A299200", "A299202", "A300383", "A300385", "A317141", "A317142", "A317775", "A317776", "A318286", "A321469", "A381078", "A381441", "A381452", "A381453", "A381454", "A381455", "A381633", "A381634", "A381635", "A381636", "A381637", "A381715", "A381716" ]
null
Gus Wiseman, Mar 06 2025
2025-03-08T12:24:03
oeisdata/seq/A381/A381452.seq
0dbdf84846f5c84c2b8b3a8a22521bae
A381453
Number of multisets that can be obtained by choosing a constant integer partition of each prime index of n and taking the multiset union.
[ "1", "1", "2", "1", "2", "2", "3", "1", "3", "2", "2", "2", "4", "3", "4", "1", "2", "3", "4", "2", "6", "2", "3", "2", "3", "4", "4", "3", "4", "4", "2", "1", "4", "2", "6", "3", "6", "4", "8", "2", "2", "6", "4", "2", "6", "3", "4", "2", "6", "3", "4", "4", "5", "4", "4", "3", "8", "4", "2", "4", "6", "2", "8", "1", "8", "4", "2", "2", "6", "6", "6", "3", "4", "6", "6", "4", "6", "8", "4", "2", "5", "2", "2", "6", "4", "4", "8" ]
[ "nonn" ]
12
1
3
[ "A000009", "A000040", "A000041", "A000079", "A000688", "A000720", "A000961", "A001055", "A001222", "A002577", "A003963", "A006171", "A008966", "A018818", "A045778", "A050320", "A050326", "A050361", "A055396", "A056239", "A061395", "A112798", "A122111", "A213242", "A213385", "A213427", "A265947", "A275870", "A279784", "A293243", "A295935", "A299200", "A300273", "A300383", "A300385", "A317141", "A321469", "A355731", "A355733", "A381078", "A381441", "A381452", "A381453", "A381454", "A381455", "A381633", "A381634", "A381635", "A381636", "A381637", "A381715", "A381716", "A381806" ]
null
Gus Wiseman, Mar 08 2025
2025-04-01T11:10:41
oeisdata/seq/A381/A381453.seq
5aca27e4cc02443c3a532a4ee0a42e8a
A381454
Number of multisets that can be obtained by choosing a strict integer partition of each prime index of n and taking the multiset union.
[ "1", "1", "1", "1", "2", "1", "2", "1", "1", "2", "3", "1", "4", "2", "2", "1", "5", "1", "6", "2", "2", "3", "8", "1", "3", "4", "1", "2", "10", "2", "12", "1", "3", "5", "4", "1", "15", "6", "4", "2", "18", "2", "22", "3", "2", "8", "27", "1", "3", "3", "5", "4", "32", "1", "6", "2", "6", "10", "38", "2", "46", "12", "2", "1", "8", "3", "54", "5", "8", "4", "64", "1", "76", "15", "3", "6", "6", "4", "89", "2", "1" ]
[ "nonn" ]
6
1
5
[ "A000009", "A000040", "A000041", "A000688", "A000720", "A001055", "A001222", "A002846", "A003586", "A003963", "A005117", "A045778", "A050320", "A050326", "A050342", "A050361", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116539", "A116540", "A122111", "A213242", "A213385", "A213427", "A265947", "A270995", "A279785", "A293243", "A293511", "A296119", "A296120", "A299200", "A299201", "A299202", "A300383", "A300385", "A317141", "A317142", "A318360", "A318361", "A321469", "A355733", "A358914", "A381078", "A381441", "A381452", "A381453", "A381454", "A381455", "A381633", "A381634", "A381635", "A381636", "A381637", "A381715", "A381716", "A381717", "A381718", "A381806" ]
null
Gus Wiseman, Mar 08 2025
2025-03-09T12:29:13
oeisdata/seq/A381/A381454.seq
21ac9168fc951997f25bf345f62a7cc2
A381455
Number of multisets that can be obtained by taking the sum of each block of a multiset partition of the prime indices of n into a multiset of constant multisets.
[ "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "5", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "7", "1", "1", "1", "4", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "1", "5", "2", "2", "1", "2", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "2", "11", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "1", "1", "1", "5", "5", "1", "1", "2", "1", "1", "1" ]
[ "nonn" ]
19
1
4
[ "A000009", "A000040", "A000041", "A000688", "A000720", "A001055", "A001222", "A002577", "A002846", "A003963", "A005117", "A006171", "A018818", "A045778", "A050320", "A050326", "A050361", "A055396", "A056239", "A061395", "A112798", "A122111", "A213242", "A213427", "A265947", "A275870", "A279784", "A289078", "A293243", "A295935", "A299200", "A299202", "A300273", "A300383", "A300385", "A317141", "A321469", "A381078", "A381441", "A381452", "A381453", "A381454", "A381455", "A381633", "A381634", "A381635", "A381636", "A381637", "A381715", "A381716" ]
null
Gus Wiseman, Mar 06 2025
2025-04-01T12:16:27
oeisdata/seq/A381/A381455.seq
30c60be23e9308a4b03345e88a88ecaa
A381456
Decimal expansion of Product_{p prime} p^(1/(p^2-1)).
[ "1", "7", "6", "8", "1", "9", "8", "0", "7", "8", "1", "5", "3", "2", "4", "4", "9", "8", "4", "1", "3", "0", "8", "5", "3", "0", "7", "7", "2", "3", "1", "4", "9", "6", "5", "5", "2", "3", "1", "2", "9", "4", "2", "2", "8", "5", "9", "1", "2", "5", "8", "9", "7", "6", "1", "2", "5", "3", "0", "1", "4", "1", "3", "7", "5", "8", "6", "1", "0", "7", "9", "1", "4", "6", "0", "0", "0", "0", "4", "3", "0", "0", "9", "3", "0", "3", "1", "5", "7", "1", "7", "1", "0", "7", "2", "8", "5", "1", "5", "6", "1", "9", "3", "8", "0", "6", "6", "6" ]
[ "cons", "nonn", "changed" ]
53
1
2
[ "A000040", "A001620", "A013661", "A074962", "A085548", "A306016", "A381456", "A381522", "A381898" ]
null
Jwalin Bhatt, Feb 24 2025
2025-04-28T00:05:12
oeisdata/seq/A381/A381456.seq
0b4923c81fcd8ae39e4f2a0e1ad0711f
A381457
Integers encoding the recursive structure of a bitonic sorter network of n elements in their binary expansion.
[ "0", "2", "5", "2762", "22325", "175338", "1405781", "187796017958058", "12026023042822997", "768764969792360106", "49208135664973067605", "3148398007269257431722", "201504853864147844281685", "12895366188400224861219498", "825310989999256684769531221" ]
[ "nonn", "base" ]
51
1
2
[ "A000217", "A001788", "A381457" ]
null
Darío Clavijo, Mar 13 2025
2025-04-01T18:12:49
oeisdata/seq/A381/A381457.seq
d56bf72ed36f5b7e15cf340b75fe448f
A381458
Primes p such that p/prev_prime(p) < 1 + (1/PrimePi(p)).
[ "19", "31", "43", "61", "73", "103", "109", "139", "151", "167", "181", "193", "197", "199", "227", "229", "233", "241", "271", "281", "283", "311", "313", "317", "349", "353", "383", "401", "421", "433", "443", "461", "463", "467", "491", "503", "523", "571", "601", "617", "619", "643", "647", "661", "677", "743", "761", "773", "811", "823", "827", "829", "857", "859", "863", "881", "883", "887", "911", "941", "971" ]
[ "nonn" ]
52
1
1
[ "A000720", "A151799", "A381458" ]
null
Alain Rocchelli, Feb 28 2025
2025-04-01T20:01:31
oeisdata/seq/A381/A381458.seq
7a88516783b3ec9092f28e47f6b311a0
A381460
Smallest n-th perfect power greater than 1 satisfying A373387(a(n)) = n.
[ "2", "49", "15625", "625", "7737809375", "735091890625", "1253790880222890625", "6634204312890625", "47312447868976594992787109375", "72624607478879073313928212890625", "471781339858152691906169456697218212890625", "1344888824246298437178134918212890625" ]
[ "nonn", "base", "hard" ]
10
1
1
[ "A018247", "A018248", "A063006", "A091661", "A091663", "A091664", "A120817", "A120818", "A290372", "A290373", "A290374", "A290375", "A317905", "A373387", "A379243", "A381460" ]
null
Marco Ripà, Feb 24 2025
2025-03-02T23:34:13
oeisdata/seq/A381/A381460.seq
5692b62e67f3246ba5dbc17a13f997d9
A381461
Number of permutations of [n] with no fixed points where adjacent elements differ by at least 3.
[ "1", "0", "0", "0", "0", "0", "2", "8", "115", "1274", "15099", "179628", "2260064", "30534802", "441269110", "6789665680", "110947884520", "1920180939650", "35099424286573", "675866037989156", "13676799446869485", "290208293166279344", "6443880771921767240" ]
[ "nonn", "more" ]
25
0
7
[ "A000166", "A002464", "A127697", "A288208", "A381461" ]
null
Alois P. Heinz, Feb 24 2025
2025-03-11T15:26:10
oeisdata/seq/A381/A381461.seq
3b28a42d88cea80d609a3f33b5c0f6e1
A381462
Limiting sequence of the possible number of inversions in stable configurations of 3^n-1 chips in a chip firing-game directed 3-ary tree resulting from a permutation-based strategy of firing chips
[ "0", "1", "3", "4", "5", "9", "10", "12", "13", "14", "15", "16", "17", "18", "27", "28", "30", "31", "32", "36", "37", "39", "40", "41", "42", "43", "44", "45", "46", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "81", "82", "84", "85", "86", "90", "91", "93", "94", "95", "96", "97", "98", "99", "108", "109", "111", "112", "113", "117", "118", "120", "121", "122", "123", "124", "125" ]
[ "nonn" ]
53
1
3
[ "A376116", "A381462", "A381463" ]
null
Ryota Inagaki, Tanya Khovanova, and Austin Luo, Feb 24 2025
2025-03-25T23:40:16
oeisdata/seq/A381/A381462.seq
e8c28f24b67d880a69fdcf777a04c093
A381463
Limiting sequence of the possible number of inversions in stable configurations of 4^n-1 chips in a chip firing-game directed 4-ary tree resulting from a permutation-based strategy of firing chips
[ "0", "1", "4", "5", "6", "16", "17", "20", "21", "22", "24", "25", "26", "27", "64", "65", "68", "69", "70", "80", "81", "84", "85", "86", "88", "89", "90", "91", "96", "97", "100", "101", "102", "104", "105", "106", "107", "108", "109", "110", "111", "112", "256", "257", "260", "261", "262", "272", "273", "276", "277", "278", "280", "281", "282", "283", "320", "321", "324", "325", "326", "336", "337", "340" ]
[ "nonn" ]
33
1
3
[ "A376116", "A381462", "A381463" ]
null
Ryota Inagaki, Tanya Khovanova, and Austin Luo, Feb 24 2025
2025-03-26T08:28:07
oeisdata/seq/A381/A381463.seq
dca53158311513b5795c17fff5a7a47d
A381464
Lexicographically earliest positive integer sequence satisfying a(n) = a(a(n))/n.
[ "1", "3", "6", "5", "20", "18", "8", "56", "10", "90", "12", "132", "14", "182", "16", "240", "19", "108", "323", "100", "22", "462", "24", "552", "26", "650", "28", "756", "30", "870", "32", "992", "34", "1122", "36", "1260", "38", "1406", "40", "1560", "42", "1722", "44", "1892", "46", "2070", "48", "2256", "50", "2450", "52", "2652", "54", "2862", "57", "448", "3135", "59", "3422", "61", "3660", "63", "3906", "65", "4160" ]
[ "nonn", "easy" ]
42
1
2
[ "A000045", "A000304", "A099267", "A257794", "A358793", "A381464" ]
null
Thomas Scheuerle, Feb 24 2025
2025-03-03T13:27:25
oeisdata/seq/A381/A381464.seq
cb492ce7fa8882e6d2deacf9f38574f6
A381465
Semiprimes k such that 6*k + 1 is also a semiprime.
[ "4", "9", "14", "15", "22", "34", "39", "49", "65", "69", "74", "82", "85", "86", "93", "94", "111", "133", "145", "158", "159", "183", "185", "194", "201", "203", "209", "214", "219", "226", "235", "259", "265", "267", "289", "299", "301", "303", "319", "321", "323", "326", "327", "334", "341", "346", "358", "361", "362", "365", "371", "377", "386", "393", "403", "407", "413", "415", "422", "427", "437", "469", "471" ]
[ "nonn" ]
12
1
1
[ "A001358", "A007693", "A111153", "A111170", "A381465" ]
null
Zak Seidov and Robert Israel, Feb 24 2025
2025-02-26T06:28:29
oeisdata/seq/A381/A381465.seq
67536663f1bb608882d4a934df25ed99
A381466
a(0) = 4; for n > 0, a(n) = a(n-1) + n if G = 1 or a(n) = n/G if G > 1, where G = gcd(a(n-1), n).
[ "4", "5", "7", "10", "2", "7", "13", "20", "2", "11", "21", "32", "3", "16", "7", "22", "8", "25", "43", "62", "10", "31", "53", "76", "6", "31", "57", "9", "37", "66", "5", "36", "8", "41", "75", "7", "43", "80", "19", "58", "20", "61", "103", "146", "22", "67", "113", "160", "3", "52", "25", "76", "13", "66", "9", "64", "7", "64", "29", "88", "15", "76", "31", "94", "32", "97", "163", "230", "34", "103", "173", "244" ]
[ "nonn" ]
37
0
1
[ "A091508", "A133058", "A381466" ]
null
Sam Chapman, Feb 24 2025
2025-03-02T10:03:34
oeisdata/seq/A381/A381466.seq
e8bdbcd7eb174cc5b5b1bfe8388edd90
A381467
Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with k cycles and no node a member of more than one cycle, 0 <= k <= floor(n/3).
[ "1", "1", "1", "1", "1", "2", "2", "3", "5", "6", "13", "1", "11", "33", "4", "23", "89", "21", "47", "240", "85", "2", "106", "657", "345", "16", "235", "1806", "1289", "109", "551", "5026", "4713", "627", "6", "1301", "13999", "16622", "3259", "64", "3159", "39260", "57535", "15576", "598", "7741", "110381", "195212", "69983", "4394", "18", "19320", "311465", "653318", "299354", "28286", "295" ]
[ "nonn", "tabf" ]
16
0
6
[ "A000055", "A001429", "A380631", "A380634", "A381467", "A381468", "A381470" ]
null
Andrew Howroyd, Feb 24 2025
2025-02-25T13:13:38
oeisdata/seq/A381/A381467.seq
ac18195db1d6b1d7d02ce98f74e09901
A381468
Number of simple connected graphs on n unlabeled nodes with no node a member of more than one cycle.
[ "1", "1", "1", "2", "4", "8", "20", "48", "133", "374", "1124", "3439", "10923", "35245", "116128", "387729", "1312038", "4485906", "15486546", "53900520", "188998450", "667062919", "2368440477", "8454560144", "30328595227", "109285433191", "395425965732", "1436219868659", "5234881134074", "19143123415166", "70216752517419" ]
[ "nonn" ]
8
0
4
[ "A000083", "A317722", "A380632", "A380805", "A381467", "A381468" ]
null
Andrew Howroyd, Feb 24 2025
2025-02-25T01:57:14
oeisdata/seq/A381/A381468.seq
9854d521614e143f31b88c44af6467b7
A381469
Number of unlabeled 2,3 cacti (triangular cacti with bridges) rooted at a triangle with n triangles and every node contained in exactly one triangle.
[ "0", "1", "1", "4", "15", "66", "304", "1503", "7622", "39856", "212447", "1151614", "6324924", "35127396", "196917025", "1112776860", "6332114208", "36252066562", "208665030299", "1206819559836", "7009605269315", "40871341270810", "239144296550695", "1403719120877546", "8263431521645830", "48774908707685849" ]
[ "nonn" ]
7
0
4
[ "A287891", "A380634", "A381469" ]
null
Andrew Howroyd, Feb 25 2025
2025-02-25T01:57:28
oeisdata/seq/A381/A381469.seq
dbdc64251bb35f39804a28d600bb3df4
A381470
Number of simple connected graphs on n unlabeled nodes with exactly 2 non-overlapping cycles.
[ "1", "4", "21", "85", "345", "1289", "4713", "16622", "57535", "195212", "653318", "2158866", "7063333", "22906699", "73742762", "235863378", "750187968", "2374249283", "7481414941", "23482536967", "73449564533", "229016163367", "712044375528", "2208131225648", "6831543467752", "21089958138852", "64978894444220" ]
[ "nonn" ]
6
6
2
[ "A000081", "A000083", "A001429", "A381467", "A381470" ]
null
Andrew Howroyd, Feb 25 2025
2025-02-25T11:37:39
oeisdata/seq/A381/A381470.seq
297da1038ccac5a19d9c9314d80280b2
A381471
Number of non-isomorphic Dynkin systems on n points.
[ "1", "1", "2", "3", "7", "13", "63", "838" ]
[ "nonn", "more" ]
7
0
3
[ "A000041", "A380571", "A381471" ]
null
Andrew Howroyd, Feb 26 2025
2025-03-05T15:08:17
oeisdata/seq/A381/A381471.seq
4442ce62c1bbdf34f249594d0c09ce22
A381472
Number of unlabeled set systems on n vertices which are closed under union of disjoint sets.
[ "1", "2", "5", "22", "345", "152589" ]
[ "nonn", "hard", "more" ]
6
0
2
[ "A000612", "A193674", "A381471", "A381472", "A381575" ]
null
Andrew Howroyd, Mar 02 2025
2025-03-05T15:08:12
oeisdata/seq/A381/A381472.seq
1a4286f1ddd49de27d93f5da7980709a
A381473
Decimal expansion of the smallest positive solution to 2*x = tan(x).
[ "1", "1", "6", "5", "5", "6", "1", "1", "8", "5", "2", "0", "7", "2", "1", "1", "3", "0", "6", "8", "3", "3", "9", "1", "7", "9", "7", "7", "9", "5", "8", "5", "6", "0", "6", "6", "9", "1", "3", "4", "5", "3", "8", "8", "4", "7", "6", "9", "3", "0", "5", "7", "2", "8", "7", "5", "5", "4", "8", "6", "8", "6", "4", "6", "6", "9", "6", "6", "1", "5", "4", "0", "8", "7", "1", "6", "3", "5", "8", "3", "3", "6", "9", "2", "1", "0", "7", "7", "1", "2", "8", "5", "5", "2", "1", "9", "6", "5", "0", "7", "0", "4", "3", "7", "2", "9", "6", "7" ]
[ "nonn", "cons" ]
7
1
3
[ "A257451", "A381473" ]
null
Andrew Howroyd, Mar 10 2025
2025-03-10T19:55:54
oeisdata/seq/A381/A381473.seq
139c66aa51c3770ff1c30e2339c053eb
A381474
Array read by antidiagonals: T(m,n) is the number of minimum connected dominating sets in the grid graph P_m X P_n.
[ "1", "2", "2", "1", "4", "1", "1", "1", "1", "1", "1", "7", "2", "7", "1", "1", "8", "1", "1", "8", "1", "1", "8", "1", "16", "1", "8", "1", "1", "8", "1", "62", "62", "1", "8", "1", "1", "8", "1", "10", "126", "10", "1", "8", "1", "1", "8", "1", "48", "11", "11", "48", "1", "8", "1", "1", "8", "1", "224", "448", "24", "448", "224", "1", "8", "1", "1", "8", "1", "8", "744", "13", "13", "744", "8", "1", "8", "1" ]
[ "nonn", "tabl" ]
9
1
2
[ "A291872", "A350820", "A381474", "A381475", "A381730" ]
null
Andrew Howroyd, Mar 19 2025
2025-03-19T18:41:40
oeisdata/seq/A381/A381474.seq
5b8f13a65398ca69a557143dfb5b24ae
A381475
Array read by antidiagonals: T(m,n) is the connected domination number of the grid graph P_m X P_n.
[ "1", "1", "1", "1", "2", "1", "2", "2", "2", "2", "3", "4", "3", "4", "3", "4", "5", "4", "4", "5", "4", "5", "6", "5", "7", "5", "6", "5", "6", "7", "6", "9", "9", "6", "7", "6", "7", "8", "7", "10", "11", "10", "7", "8", "7", "8", "9", "8", "12", "12", "12", "12", "8", "9", "8", "9", "10", "9", "14", "15", "14", "15", "14", "9", "10", "9", "10", "11", "10", "15", "17", "16", "16", "17", "15", "10", "11", "10" ]
[ "nonn", "tabl" ]
6
1
5
[ "A300358", "A350823", "A369692", "A381474", "A381475" ]
null
Andrew Howroyd, Mar 19 2025
2025-03-19T18:42:37
oeisdata/seq/A381/A381475.seq
95f1f4a57c650adaa562a8298ff84e11
A381476
Triangle read by rows: T(n,k) is the number of subsets of {1..n} with k elements such that every pair of distinct elements has a different difference, 0 <= k <= A143824(n).
[ "1", "1", "1", "1", "2", "1", "1", "3", "3", "1", "4", "6", "2", "1", "5", "10", "6", "1", "6", "15", "14", "1", "7", "21", "26", "2", "1", "8", "28", "44", "10", "1", "9", "36", "68", "26", "1", "10", "45", "100", "60", "1", "11", "55", "140", "110", "1", "12", "66", "190", "190", "4", "1", "13", "78", "250", "304", "22", "1", "14", "91", "322", "466", "68", "1", "15", "105", "406", "676", "156" ]
[ "nonn", "tabf" ]
9
0
5
[ "A000012", "A001477", "A003022", "A143823", "A143824", "A161680", "A212964", "A241688", "A241689", "A241690", "A325879", "A381476", "A382395" ]
null
Andrew Howroyd, Mar 27 2025
2025-03-27T21:31:40
oeisdata/seq/A381/A381476.seq
3994b4eda55ed1177eff383a3fb50045
A381477
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cosh(x * A(x)^2) ).
[ "1", "1", "6", "75", "1440", "37445", "1231440", "49037527", "2294425728", "123393443049", "7500623201280", "508577491719011", "38057966976387072", "3115680296111519149", "277005128553759191040", "26579020362900758232495", "2737628961211699538657280", "301278578823933606439917137", "35281158151116225085977526272" ]
[ "nonn" ]
8
0
3
[ "A185951", "A364985", "A381386", "A381477" ]
null
Seiichi Manyama, Feb 24 2025
2025-02-25T06:43:56
oeisdata/seq/A381/A381477.seq
78117df799414045a8a4f884fa715dfe
A381478
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cosh(x * A(x)) )^2.
[ "1", "2", "14", "186", "3696", "98290", "3283920", "132311354", "6246905728", "338374946466", "20688891816960", "1409607482926522", "105914955915952128", "8701156803022552466", "775923181679913938944", "74646655589398509637050", "7706371729268071660093440", "849834260414107910987980354" ]
[ "nonn" ]
12
0
2
[ "A185951", "A377546", "A381387", "A381449", "A381477", "A381478" ]
null
Seiichi Manyama, Feb 24 2025
2025-02-25T01:58:01
oeisdata/seq/A381/A381478.seq
0b4b62822ab75916f46734cea2b75275
A381479
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cos(x * A(x)^2) ).
[ "1", "1", "6", "69", "1200", "28085", "828240", "29502473", "1232606592", "59114482569", "3201204188160", "193215861134989", "12862437022076928", "936256855741871677", "73978404781917941760", "6306254322850544942865", "576881179288397985054720", "56369243043268551691136657", "5859726074013471622734938112" ]
[ "nonn" ]
8
0
3
[ "A185951", "A364985", "A381388", "A381479" ]
null
Seiichi Manyama, Feb 24 2025
2025-02-25T01:58:36
oeisdata/seq/A381/A381479.seq
9eb8f0c7181392dcd07724e12e5fcb37
A381480
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cos(x * A(x)) )^2.
[ "1", "2", "14", "174", "3168", "76450", "2304720", "83473726", "3533382272", "171254814210", "9355068840960", "568799458870478", "38102773549750272", "2788540163472852386", "221380225364522119168", "18950242574522637197790", "1739955233454599038402560", "170582215179135413189856514", "17785491645892269582026145792" ]
[ "nonn" ]
10
0
2
[ "A185951", "A381478", "A381480" ]
null
Seiichi Manyama, Feb 24 2025
2025-02-25T01:59:05
oeisdata/seq/A381/A381480.seq
ddf5b824006a2d3e61e84f30374e36af
A381481
Dirichlet g.f.: zeta(s) * Product_{p prime} (1 - 1/p^(2*s) - 1/p^(3*s)).
[ "1", "1", "1", "0", "1", "1", "1", "-1", "0", "1", "1", "0", "1", "1", "1", "-1", "1", "0", "1", "0", "1", "1", "1", "-1", "0", "1", "-1", "0", "1", "1", "1", "-1", "1", "1", "1", "0", "1", "1", "1", "-1", "1", "1", "1", "0", "0", "1", "1", "-1", "0", "0", "1", "0", "1", "-1", "1", "-1", "1", "1", "1", "0", "1", "1", "0", "-1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "-1", "-1", "1", "1", "0", "1", "1", "1", "-1", "1", "0", "1", "0", "1", "1", "1", "-1", "1", "0", "0", "0" ]
[ "sign", "mult", "easy", "new" ]
22
1
null
[ "A013661", "A065470", "A299406", "A365498", "A380922", "A381481", "A383292" ]
null
Vaclav Kotesovec, Apr 22 2025
2025-04-22T11:06:58
oeisdata/seq/A381/A381481.seq
b160a9b366669ec6ede6ae157214077d
A381482
a(n) = Sum_{k=0..floor(n/2)} binomial(n,k)^2 * binomial(n-k,k) * 2^k.
[ "1", "1", "9", "37", "241", "1401", "8961", "57429", "377217", "2509201", "16876729", "114600069", "783903121", "5397915433", "37372017489", "259998843477", "1816376953857", "12736545070113", "89602978644969", "632223913939557", "4472680961409201", "31717890254271321", "225416254500886689", "1605197563027768917" ]
[ "nonn", "new" ]
12
0
3
[ "A001045", "A001850", "A084601", "A206178", "A275027", "A381482" ]
null
Ilya Gutkovskiy, Apr 22 2025
2025-04-23T10:55:22
oeisdata/seq/A381/A381482.seq
0e9b0a71040a6b09886d168e6a8714e8
A381484
Expansion of e.g.f. exp(-x/3) / (1-3*x)^(1/9).
[ "1", "0", "1", "6", "57", "708", "10905", "200538", "4287633", "104507496", "2860291089", "86853807630", "2897638853769", "105357244427244", "4146601837761513", "175632278607964962", "7965651564924845985", "385161391574120046672", "19778647046883844762017", "1074979845580061777989014" ]
[ "nonn", "new" ]
29
0
4
[ "A000166", "A381484", "A381504", "A383313" ]
null
Seiichi Manyama, Apr 23 2025
2025-04-23T10:19:45
oeisdata/seq/A381/A381484.seq
ce3ac40a8e5d988bdc009b85320191c6
A381485
Decimal expansion of sqrt(13)/6.
[ "6", "0", "0", "9", "2", "5", "2", "1", "2", "5", "7", "7", "3", "3", "1", "5", "4", "8", "8", "5", "3", "2", "0", "3", "5", "4", "4", "5", "7", "8", "4", "1", "5", "9", "9", "1", "0", "4", "1", "8", "8", "2", "7", "6", "2", "3", "0", "7", "5", "4", "1", "0", "3", "5", "4", "5", "1", "7", "4", "2", "1", "7", "6", "0", "3", "7", "8", "6", "1", "1", "5", "8", "0", "4", "8", "8", "3", "5", "0", "7", "4", "2", "0", "0", "7", "6", "9", "8", "4", "7", "0", "0", "3", "0", "8", "1", "7", "8", "6", "2", "7", "8", "9", "1", "9" ]
[ "nonn", "cons", "easy" ]
5
0
1
[ "A002193", "A010470", "A010503", "A020761", "A101263", "A120683", "A142464", "A176019", "A281065", "A295330", "A344069", "A379338", "A381485" ]
null
Amiram Eldar, Feb 24 2025
2025-02-25T02:29:54
oeisdata/seq/A381/A381485.seq
bcb319e6749a7f88d655713e03e06a8d
A381486
Number of labeled histories for rooted ternary trees with 2n+1 leaves if simultaneous trifurcations are allowed.
[ "1", "1", "10", "420", "43960", "9347800", "3513910400", "2131249120000", "1952028782704000", "2568150610833808000", "4666919676058159520000", "11351087418588355518080000", "36008099327884173922432000000", "145785514242304854141480256000000", "739598808823839440680777500928000000", "4627885522642342503645368137231360000000" ]
[ "nonn" ]
15
0
3
[ "A317059", "A339411", "A381486" ]
null
Noah A Rosenberg, Feb 25 2025
2025-02-26T09:51:30
oeisdata/seq/A381/A381486.seq
fd6917f7d802d12f0c353f73a268a144
A381487
Numbers which are a power of their digital root.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "81", "128", "256", "512", "729", "2401", "6561", "8192", "16384", "32768", "59049", "78125", "524288", "531441", "823543", "1048576", "2097152", "4782969", "33554432", "43046721", "67108864", "134217728", "282475249", "387420489", "1220703125", "2147483648", "3486784401", "4294967296" ]
[ "nonn", "base" ]
26
1
3
[ "A000012", "A010689", "A010734", "A010888", "A023106", "A070366", "A070403", "A100401", "A100402", "A100403", "A153130", "A381487", "A381491", "A381492" ]
null
Stefano Spezia, Feb 25 2025
2025-02-27T07:12:07
oeisdata/seq/A381/A381487.seq
9c48c1358bc5a59e6405592bb268034d
A381488
Pentagonal numbers that are deficient.
[ "1", "5", "22", "35", "51", "92", "117", "145", "247", "287", "376", "425", "477", "590", "651", "715", "782", "925", "1001", "1162", "1247", "1335", "1426", "1617", "1717", "2035", "2147", "2501", "2625", "2882", "3015", "3151", "3577", "3725", "4187", "4347", "4845", "5017", "5551", "5735", "6112", "6305", "6501", "6902", "7107", "7315", "7526", "7957" ]
[ "nonn" ]
20
1
2
[ "A000326", "A005100", "A379264", "A381488" ]
null
Massimo Kofler, Feb 25 2025
2025-03-03T12:42:52
oeisdata/seq/A381/A381488.seq
32d4a887e1506d07741cda82541f432b
A381489
Index of first half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.
[ "0", "0", "1", "1", "2", "2", "3", "3", "0", "0", "1", "1", "2", "2", "3", "3", "4", "4", "5", "5", "6", "6", "7", "7", "4", "4", "5", "5", "6", "6", "7", "7", "0", "0", "1", "1", "2", "2", "3", "3", "0", "0", "1", "1", "2", "2", "3", "3", "4", "4", "5", "5", "6", "6", "7", "7", "4", "4", "5", "5", "6", "6", "7", "7", "0", "0", "1", "1", "2", "2", "3", "3", "0", "0", "1", "1", "2", "2", "3", "3", "4", "4", "5", "5", "6", "6", "7", "7", "4", "4", "5", "5", "6", "6", "7", "7" ]
[ "easy", "nonn" ]
22
0
5
[ "A380008", "A380009", "A381489", "A381490" ]
null
Luis Rato, Feb 25 2025
2025-03-21T02:24:18
oeisdata/seq/A381/A381489.seq
29591f9d6d73ed8072123c9fa68896cb
A381490
Index of second half of decomposition of integers into pairs x(i)+y(j) based on A380008 and A380009, respectively.
[ "0", "1", "0", "1", "0", "1", "0", "1", "2", "3", "2", "3", "2", "3", "2", "3", "0", "1", "0", "1", "0", "1", "0", "1", "2", "3", "2", "3", "2", "3", "2", "3", "4", "5", "4", "5", "4", "5", "4", "5", "6", "7", "6", "7", "6", "7", "6", "7", "4", "5", "4", "5", "4", "5", "4", "5", "6", "7", "6", "7", "6", "7", "6", "7", "8", "9", "8", "9", "8", "9", "8", "9", "10", "11", "10", "11", "10", "11", "10", "11", "8", "9", "8", "9", "8", "9", "8", "9" ]
[ "easy", "nonn" ]
15
0
9
[ "A380008", "A380009", "A381489", "A381490" ]
null
Luis Rato, Feb 25 2025
2025-03-06T14:45:34
oeisdata/seq/A381/A381490.seq
07e81cb80ec5804132e96eead6f0c3ba
A381491
a(n) = A010888(A381487(n)).
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "9", "2", "4", "8", "9", "7", "9", "2", "4", "8", "9", "5", "2", "9", "7", "4", "8", "9", "2", "9", "4", "8", "7", "9", "5", "2", "9", "4", "8", "9", "7", "2", "4", "9", "8", "9", "2", "4", "5", "9", "7", "8", "9", "2", "4", "9", "8", "7", "9", "2", "4", "8", "9", "5", "9", "2", "7", "4", "8", "9", "9", "2", "4", "8", "9", "7", "5", "9", "2", "4", "8", "9", "7", "2", "9", "4", "8", "9" ]
[ "nonn", "base" ]
17
1
3
[ "A010888", "A381487", "A381491", "A381492" ]
null
Stefano Spezia, Feb 25 2025
2025-02-27T10:48:48
oeisdata/seq/A381/A381491.seq
65959eb8648122b2cf833712326bdce8
A381492
a(n) is the logarithm to base A381491(n) of A381487(n).
[ "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "7", "4", "3", "3", "4", "4", "13", "7", "5", "5", "7", "19", "6", "7", "10", "7", "7", "25", "8", "13", "9", "10", "9", "13", "31", "10", "16", "11", "11", "13", "37", "19", "12", "13", "13", "43", "22", "19", "14", "16", "15", "15", "49", "25", "16", "17", "19", "17", "55", "28", "19", "18", "25", "19", "61", "22", "31", "21", "20", "21", "67", "34", "23", "22", "25" ]
[ "nonn", "base" ]
16
1
11
[ "A381487", "A381491", "A381492" ]
null
Stefano Spezia, Feb 25 2025
2025-02-27T10:48:03
oeisdata/seq/A381/A381492.seq
6a26c8a7d7c021f0f4c065886c6cceaf
A381493
Smallest number with reciprocal of period length n in base 8.
[ "1", "7", "3", "73", "5", "31", "19", "49", "17", "262657", "11", "23", "37", "79", "43", "631", "97", "103", "81", "32377", "25", "3577", "67", "47", "323", "601", "237", "2593", "29", "233", "209", "2147483647", "193", "199", "307", "71", "405", "223", "571", "937", "187", "13367", "817", "431", "115", "271", "139", "2351", "577", "343", "251" ]
[ "nonn", "base" ]
15
0
2
[ "A003060", "A379641", "A381493" ]
null
Erich Friedman, Feb 25 2025
2025-02-28T15:13:53
oeisdata/seq/A381/A381493.seq
819d64317ef09cf2be504f0a4ecb0b9c
A381494
Smallest number with reciprocal of period length n in base 7.
[ "1", "2", "4", "9", "5", "2801", "36", "29", "64", "27", "11", "1123", "13", "16148168401", "113", "31", "17", "14009", "108", "419", "55", "261", "23", "47", "73", "2551", "53", "81", "145", "59", "99", "311", "256", "3631", "56036", "81229", "135", "223", "1676", "486643", "41", "83", "1017", "166003607842448777", "115", "837", "188", "13722816749522711", "153", "3529", "10204" ]
[ "nonn", "base" ]
17
0
2
[ "A003060", "A379640", "A381494" ]
null
Erich Friedman, Feb 25 2025
2025-03-03T09:32:16
oeisdata/seq/A381/A381494.seq
91c3a2982b01bfdac68360b1bd4620b9
A381495
a(n) is the number of times n appears in A381466.
[ "0", "2", "2", "1", "3", "1", "5", "2", "3", "2", "2", "0", "2", "0", "2", "1", "0", "1", "4", "2", "3", "2", "3", "1", "6", "0", "1", "0", "4", "0", "5", "2", "0", "1", "0", "1", "6", "0", "4", "1", "3", "2", "3", "1", "1", "0", "2", "1", "0", "0", "2", "2", "4", "1", "3", "0", "4", "1", "4", "1", "4", "1", "1", "3", "1", "4", "2", "0", "1", "1", "2", "1", "3", "0", "2", "3", "3", "1", "2", "3", "1", "1", "2", "1", "0", "0", "2", "1", "1", "2", "4", "0", "0", "2", "1", "0", "3", "0", "2", "1", "2", "1", "2", "0", "0", "0", "3", "2", "3", "0", "3", "1", "3", "1", "1", "2", "4", "1", "3", "1", "3", "0", "1", "0", "2", "1", "4", "1", "1", "1" ]
[ "nonn" ]
19
1
2
[ "A381466", "A381495", "A381501" ]
null
Sam Chapman, Feb 25 2025
2025-03-09T16:40:21
oeisdata/seq/A381/A381495.seq
35beb6fd309d031a5c42f05f8996a2d6
A381496
Number of powerful numbers that are not prime powers that do not exceed 10^n.
[ "0", "0", "3", "28", "133", "510", "1790", "5997", "19639", "63541", "204037", "652173", "2078320", "6609816", "20993381", "66612867", "211222374", "669428537", "2120835892", "6717184256", "21270247404", "67341572823", "213173925948", "674739560651", "2135491756895", "6758117426102", "21385762133815", "67670426242420" ]
[ "nonn" ]
23
0
3
[ "A001694", "A118896", "A126706", "A246547", "A267574", "A286708", "A380430", "A380431", "A381391", "A381496" ]
null
Michael De Vlieger, Feb 25 2025
2025-04-02T03:05:25
oeisdata/seq/A381/A381496.seq
d57dffe4b28f56a4449efe9618a4a9ae
A381497
a(n) = sum of numbers k < n such that 1 < gcd(k,n) and rad(k) != rad(n), where rad = A007947.
[ "0", "0", "0", "0", "0", "9", "0", "6", "6", "25", "0", "36", "0", "49", "45", "42", "0", "81", "0", "100", "84", "121", "0", "144", "45", "169", "96", "196", "0", "315", "0", "210", "198", "289", "175", "354", "0", "361", "273", "430", "0", "609", "0", "484", "435", "529", "0", "648", "140", "655", "459", "676", "0", "801", "385", "826", "570", "841", "0", "1260", "0", "961", "798" ]
[ "nonn" ]
11
1
6
[ "A007947", "A038566", "A066760", "A067392", "A121998", "A369609", "A381094", "A381096", "A381497", "A381498", "A381499" ]
null
Michael De Vlieger, Mar 02 2025
2025-03-07T09:07:10
oeisdata/seq/A381/A381497.seq
ff9a156e53245fc6e204e89070e8c3b4
A381498
a(n) = sum of numbers k <= n that have the same squarefree kernel as n.
[ "1", "2", "3", "6", "5", "6", "7", "14", "12", "10", "11", "18", "13", "14", "15", "30", "17", "36", "19", "30", "21", "22", "23", "60", "30", "26", "39", "42", "29", "30", "31", "62", "33", "34", "35", "96", "37", "38", "39", "70", "41", "42", "43", "66", "60", "46", "47", "144", "56", "120", "51", "78", "53", "198", "55", "98", "57", "58", "59", "90", "61", "62", "84", "126", "65", "66" ]
[ "nonn" ]
7
1
2
[ "A007947", "A008479", "A244974", "A369609", "A381498" ]
null
Michael De Vlieger, Mar 03 2025
2025-03-07T09:07:23
oeisdata/seq/A381/A381498.seq
66ee8178420f3b8094e9b1a89fed7627
A381499
a(n) = sum of numbers k < n such that 1 < gcd(k,n) < k and rad(k) does not divide n, where rad = A007947.
[ "0", "0", "0", "0", "0", "0", "0", "6", "6", "6", "0", "10", "0", "28", "28", "42", "0", "39", "0", "65", "65", "80", "0", "102", "45", "126", "96", "159", "0", "111", "0", "210", "148", "210", "138", "253", "0", "280", "221", "338", "0", "342", "0", "411", "366", "444", "0", "547", "140", "563", "403", "601", "0", "700", "344", "708", "512", "750", "0", "751", "0", "868", "703", "930" ]
[ "nonn" ]
7
1
8
[ "A007947", "A038566", "A066760", "A121998", "A243823", "A272619", "A381497", "A381499" ]
null
Michael De Vlieger, Mar 02 2025
2025-03-07T09:07:33
oeisdata/seq/A381/A381499.seq
b65c6f79de3fa6af1e320fd53888bf22
A381500
a(n) = A019565(A187769(n)).
[ "1", "2", "3", "6", "5", "10", "15", "30", "7", "14", "21", "35", "42", "70", "105", "210", "11", "22", "33", "55", "77", "66", "110", "165", "154", "231", "385", "330", "462", "770", "1155", "2310", "13", "26", "39", "65", "91", "143", "78", "130", "195", "182", "273", "455", "286", "429", "715", "1001", "390", "546", "910", "1365", "858", "1430", "2145", "2002", "3003" ]
[ "nonn", "base", "easy" ]
17
0
2
[ "A002110", "A019565", "A098012", "A119416", "A163866", "A187769", "A253550", "A294648", "A344085", "A381500" ]
null
Michael De Vlieger, Peter Munn, and Antti Karttunen, Feb 27 2025
2025-03-07T11:34:17
oeisdata/seq/A381/A381500.seq
25bac0aa4b7ffb6f0e110ea442fcb321
A381501
Positive integers that do not appear in A381466.
[ "1", "12", "14", "17", "26", "28", "30", "33", "35", "38", "46", "49", "50", "56", "68", "74", "85", "86", "92", "93", "96", "98", "104", "105", "106", "110", "122", "124", "132", "134", "140", "156", "164", "166", "170", "182", "188", "190", "194", "195", "200", "202", "214", "218", "226", "236", "242", "248", "250", "254", "260", "284", "285", "290", "302", "304", "305", "308", "310", "314", "320", "326", "336", "338", "344", "346", "350", "362", "368", "374", "375" ]
[ "nonn" ]
25
1
2
[ "A381466", "A381495", "A381501" ]
null
Sam Chapman, Feb 25 2025
2025-03-20T04:35:24
oeisdata/seq/A381/A381501.seq
25cc0e5ad61bd3684b0f44a9069a2ad7
A381502
a(n) is the smallest number k such that with x(1) = k and x(i+1) = 2*x(i) + 1, x(i+1) has exactly one more prime factor (counted with multiplicity) than x(i) for i = 1 to n but not i = n + 1.
[ "2", "1", "87", "43", "197161", "8651161" ]
[ "nonn", "more" ]
10
1
1
[ "A001222", "A381502" ]
null
Robert Israel, Feb 25 2025
2025-02-27T07:58:20
oeisdata/seq/A381/A381502.seq
2f221753bef1177add148c76d42ba3ce
A381503
Number of rectangles in a Fibonacci(n) X Fibonacci(n+1) grid.
[ "1", "3", "18", "90", "540", "3276", "21021", "137445", "916300", "6167700", "41812200", "284604840", "1942428033", "13278352815", "90862598190", "622150990734", "4261620339460", "29198279495220", "200080147593645", "1371167039301345", "9397260307853496", "64406143791454248", "441430873666787088", "3025546968019741200" ]
[ "nonn", "easy" ]
18
1
2
[ "A000045", "A033192", "A096948", "A377704", "A381503" ]
null
Darío Clavijo, Feb 25 2025
2025-03-14T21:19:30
oeisdata/seq/A381/A381503.seq
4a612ae3a96d4d5fd1f2ab3be2e6405d
A381504
Expansion of e.g.f. exp(-x/4) / (1-4*x)^(1/16).
[ "1", "0", "1", "8", "99", "1616", "32815", "797256", "22552873", "728069984", "26413495281", "1063820511080", "47098650935611", "2273501091042288", "118834339196361919", "6686552010270859496", "402975635704196998545", "25897425517232941658816", "1767875520978811381774753", "127753191169784612437640904" ]
[ "nonn", "new" ]
15
0
4
[ "A000166", "A381484", "A381504", "A383313" ]
null
Seiichi Manyama, Apr 23 2025
2025-04-23T10:17:25
oeisdata/seq/A381/A381504.seq
d54002f3386e0f13e6fa493abf4caa2e
A381505
Expansion of e.g.f. exp(2*x/3) / (1-3*x)^(1/9).
[ "1", "1", "2", "10", "88", "1064", "16144", "293968", "6241280", "151328512", "4124855296", "124843943936", "4153947277312", "150699794606080", "5919989155033088", "250339939417452544", "11338037538551824384", "547552961327680913408", "28087260712728645468160", "1525087432592278987866112" ]
[ "nonn", "new" ]
13
0
3
[ "A002801", "A381505", "A381506" ]
null
Seiichi Manyama, Apr 23 2025
2025-04-23T10:14:45
oeisdata/seq/A381/A381505.seq
093c98217e0af907609b40f89369dc06
A381506
Expansion of e.g.f. exp(3*x/4) / (1-4*x)^(1/16).
[ "1", "1", "2", "12", "138", "2202", "44172", "1064664", "29947644", "962720316", "34812065304", "1398413067984", "61779789904248", "2976866834860728", "155364530441352912", "8730749828092965408", "525584335643810008848", "33743905825099188235536", "2301524700814009677800736" ]
[ "nonn", "new" ]
13
0
3
[ "A002801", "A381505", "A381506" ]
null
Seiichi Manyama, Apr 23 2025
2025-04-23T10:12:13
oeisdata/seq/A381/A381506.seq
b8e9b7231168d5dd0fbfed3d2caade78
A381507
Squarefree numbers k such that the sum of 1/(p-1) over the prime divisors p of k is 1.
[ "2", "1365", "73815", "6702045", "8788065", "26241285", "32426205", "237539445", "269409855", "445317015", "475231515", "709296105", "1085962395", "1329722835", "1447857915", "2403281595", "3255993615", "5145721455", "5254163355", "5824953435", "6560751435", "7176232455", "7703697855", "8332635255", "8542035645" ]
[ "nonn", "new" ]
25
1
1
[ "A005117", "A380888", "A381507" ]
null
Robert Israel, Apr 23 2025
2025-04-27T09:50:01
oeisdata/seq/A381/A381507.seq
f44baa8ea04f64c7af0fa728ea737e62
A381508
Pisano period of Hexanacci numbers (A001592) mod n.
[ "1", "7", "728", "14", "208", "728", "342", "28", "2184", "1456", "354312", "728", "9520", "2394", "1456", "56", "709928", "2184", "5227320", "1456", "124488", "354312", "279840", "728", "1040", "9520", "6552", "2394", "243880", "1456", "71040", "112", "4606056", "4969496", "35568", "2184", "20362908", "5227320", "123760", "1456", "201840" ]
[ "nonn", "new" ]
40
1
2
[ "A001175", "A001592", "A381508" ]
null
Martin Guerra and Doron Zeilberger, Apr 24 2025
2025-04-26T10:25:06
oeisdata/seq/A381/A381508.seq
5db27b37dd61024020744384e4d3637a
A381509
Numbers whose nonzero digits are in nondecreasing order and any zeros appear at the end.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "22", "23", "24", "25", "26", "27", "28", "29", "30", "33", "34", "35", "36", "37", "38", "39", "40", "44", "45", "46", "47", "48", "49", "50", "55", "56", "57", "58", "59", "60", "66", "67", "68", "69", "70", "77", "78", "79", "80", "88", "89", "90", "99", "100", "110", "111", "112", "113", "114", "115", "116", "117" ]
[ "nonn", "base", "easy", "new" ]
16
1
3
[ "A179239", "A381509" ]
null
Keenin D. Krehbiel, Feb 25 2025
2025-04-18T19:08:54
oeisdata/seq/A381/A381509.seq
4fe0d9446623dde693c1c04764d372bf
A381510
Smaller of two consecutive primes p and q, both ending with 7, such that q - p = 10n, or -1 if no such primes exist.
[ "337", "887", "4297", "33247", "31907", "124367", "218287", "1122287", "1964987", "1313467", "1468277", "7160227", "5518687", "16525757", "13626257", "71880637", "27915737", "17051707", "394059907", "566348087", "252314747", "472865287", "1289694257", "633418787", "1588640437", "944192807", "1391048047", "7059848287" ]
[ "nonn", "base" ]
21
1
1
[ "A101232", "A140791", "A380785", "A381372", "A381510" ]
null
Jean-Marc Rebert, Feb 25 2025
2025-03-10T12:03:10
oeisdata/seq/A381/A381510.seq
f3d934b090f2250cab061561194da5ca
A381511
Smaller of two consecutive primes p and q, both ending with 9, such that q - p = 10*n, or -1 if no such primes exist.
[ "139", "3089", "5749", "20809", "60539", "110359", "173359", "618719", "1294849", "838249", "6877109", "1895359", "11188759", "7621259", "35560009", "33803689", "124956059", "92801029", "142414669", "378043979", "229316459", "390932389", "1095750599", "995151679", "2174082649", "2603726969", "3402493709", "1997191249" ]
[ "nonn", "base" ]
20
1
1
[ "A101232", "A140791", "A380785", "A381372", "A381510", "A381511" ]
null
Jean-Marc Rebert, Feb 25 2025
2025-03-09T12:24:06
oeisdata/seq/A381/A381511.seq
8f5f5a402b57869034161ff467c3d675
A381514
a(n) is the hafnian of a symmetric Toeplitz matrix of order 2*n whose off-diagonal element (i,j) equals the |i-j|-th prime.
[ "1", "2", "23", "899", "85072", "15120411", "4439935299", "1989537541918", "1264044973158281", "1090056235155152713", "1227540523199054294506" ]
[ "nonn", "hard", "more" ]
10
0
2
[ "A071078", "A071079", "A085807", "A306457", "A318173", "A356483", "A374067", "A374068", "A381514" ]
null
Stefano Spezia, Feb 25 2025
2025-02-26T18:12:02
oeisdata/seq/A381/A381514.seq
fd071baf1629c2b8b465804764f686f5
A381515
a(n) = Sum_{j=1..n} Stirling2(n-1,j-1) * a(n-j) for n>=1, starting with a(0) = 1.
[ "1", "1", "1", "2", "5", "16", "71", "432", "3446", "35805", "493247", "9055817", "219034736", "6924788187", "287364757172", "15747872749912", "1138063678023858", "107917571120653077", "13417659577126888599", "2194989270698166806727", "473329783091262653789042", "134287984058139116699933228" ]
[ "nonn" ]
12
0
4
[ "A000110", "A008277", "A048993", "A308444", "A381515" ]
null
Alois P. Heinz, Feb 25 2025
2025-02-26T09:50:02
oeisdata/seq/A381/A381515.seq
5c7b7499a532ae478d14f5dd6deb2888
A381516
a(n) = 1 + number of divisors of n within the sequence up to a(n-1).
[ "1", "2", "3", "3", "3", "2", "7", "3", "4", "6", "4", "2", "12", "2", "7", "6", "8", "2", "13", "2", "10", "8", "8", "2", "21", "2", "11", "6", "14", "2", "19", "2", "17", "7", "13", "5", "22", "2", "14", "8", "21", "2", "28", "2", "19", "7", "15", "2", "30", "6", "18", "7", "20", "2", "26", "4", "32", "8", "17", "2", "35", "2", "19", "13", "28", "6", "30", "2", "25", "6", "30", "2", "41", "2", "22", "9", "28", "8", "36", "2", "35" ]
[ "nonn" ]
18
0
2
[ "A027750", "A056148", "A381516" ]
null
Austin Blake, Feb 25 2025
2025-03-29T04:27:35
oeisdata/seq/A381/A381516.seq
57891208bbb216a9f2a75a76ef27939c
A381517
Perimeter of the Sierpiński carpet at iteration n.
[ "4", "16", "80", "496", "3536", "26992", "212048", "1684720", "13442768", "107437168", "859182416", "6872514544", "54977282000", "439809752944", "3518452514384", "28147543587568", "225180119118032", "1801440264196720", "14411520047331152", "115292154179921392", "922337214843187664", "7378697662956950896", "59029581136289955920", "472236648588222693616" ]
[ "nonn", "easy" ]
80
0
1
[ "A001018", "A113210", "A271939", "A293143", "A365606", "A381517" ]
null
Jakub Buczak, Feb 26 2025
2025-03-02T08:02:32
oeisdata/seq/A381/A381517.seq
45fe0a7fa43eb5ef3747ff688ca58267
A381518
Expansion of e.g.f. ( (1/x) * Series_Reversion( x/(1 + sin(x))^2 ) )^(1/2).
[ "1", "1", "4", "29", "304", "4141", "68832", "1337881", "29432576", "712263961", "18403873280", "487814777141", "12296236382208", "230142147098501", "-2906327530115072", "-800177574047914831", "-75835523291585773568", "-6054072134316123116495", "-459749417224473755910144", "-34556942957229166465685555" ]
[ "sign" ]
8
0
3
[ "A136630", "A198865", "A381518", "A381519" ]
null
Seiichi Manyama, Feb 26 2025
2025-02-26T06:26:45
oeisdata/seq/A381/A381518.seq
db14d2aaf0d17a979dd2ef6639c1bb1d
A381519
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sin(x))^2 ).
[ "1", "2", "10", "82", "936", "13642", "240656", "4952218", "115608704", "2992207250", "84070140672", "2507383885730", "77117178496000", "2329071118971482", "61202811821836288", "690380688651775978", "-88097620429234470912", "-11900508444760552311518", "-1112180862634722333884416" ]
[ "sign" ]
11
0
2
[ "A136630", "A377553", "A381389", "A381442", "A381449", "A381518", "A381519", "A381521" ]
null
Seiichi Manyama, Feb 26 2025
2025-02-26T06:26:17
oeisdata/seq/A381/A381519.seq
657c633348de3b9688ae03483d83a22b
A381520
Expansion of e.g.f. ( (1/x) * Series_Reversion( x/(1 + x * cos(x))^2 ) )^(1/2).
[ "1", "1", "4", "27", "240", "2345", "17280", "-226597", "-21007616", "-1007159823", "-42976972800", "-1775328986981", "-72123329507328", "-2843431148886887", "-103621659777126400", "-2971936506262036965", "-6719764584265482240", "9528526268302653725537", "1192610999728818101551104" ]
[ "sign" ]
12
0
3
[ "A185951", "A381378", "A381447", "A381479", "A381520" ]
null
Seiichi Manyama, Feb 26 2025
2025-02-26T06:26:26
oeisdata/seq/A381/A381520.seq
1b3717d5d1c01ed05d36b65d6ffbe3e4
A381521
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x * cos(x))^2 ).
[ "1", "2", "10", "78", "792", "9250", "106080", "636286", "-30646784", "-2237508990", "-112000654080", "-5124930562642", "-227068649702400", "-9819508698442846", "-406371251899045888", "-15094508095346343330", "-394372545425757634560", "7096803535075158290434", "2430273114806112504446976" ]
[ "sign" ]
11
0
2
[ "A185951", "A377553", "A381442", "A381449", "A381480", "A381519", "A381520", "A381521" ]
null
Seiichi Manyama, Feb 26 2025
2025-02-26T06:26:36
oeisdata/seq/A381/A381521.seq
9f85b46f3a1cb197886df0b237db990b
A381522
a(n) = k after every k^2 occurrences of 1, with multiple values following a 1 listed in order.
[ "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "3", "1", "1", "1", "2", "1", "1", "1", "1", "2", "4", "1", "1", "3", "1", "1", "2", "1", "1", "1", "1", "2", "1", "5", "1", "1", "3", "1", "2", "1", "1", "1", "1", "2", "4", "1", "1", "1", "1", "2", "3", "6", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "3", "1", "1", "1", "2", "4", "1", "7", "1", "5", "1", "1", "2", "1", "1", "3", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "3", "1", "2", "4", "8", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "3", "6" ]
[ "nonn", "changed" ]
36
1
5
[ "A000188", "A084580", "A381456", "A381522", "A381900", "A382093" ]
null
Jwalin Bhatt, Feb 26 2025
2025-04-15T21:42:09
oeisdata/seq/A381/A381522.seq
162fae851c7a624094b4b7b9dad75b76
A381523
Number of labeled histories for rooted 4-furcating trees with 3n+1 leaves if simultaneous 4-furcations are allowed.
[ "1", "1", "35", "8925", "8033025", "19010866875", "97622651251125", "958647115051250625", "16437666902498106890625", "459581350409578975249546875", "19861812620603175030206132109375", "1271123241419341933758758697996796875", "116303414318027015186301064741488195703125", "14773177703549629967524262172307456486365234375" ]
[ "nonn" ]
7
0
3
[ "A317059", "A381486", "A381523" ]
null
Noah A Rosenberg, Feb 26 2025
2025-02-26T09:51:17
oeisdata/seq/A381/A381523.seq
16e40d612ab15c5482040b3ab9301287
A381524
Smallest exponent of x of maximal coefficient (ignoring signs) in Hermite polynomial of order n.
[ "0", "1", "2", "1", "2", "3", "2", "3", "2", "3", "4", "3", "4", "3", "4", "5", "4", "5", "4", "5", "6", "5", "6", "5", "6", "5", "6", "7", "6", "7", "6", "7", "6", "7", "6", "7", "8", "7", "8", "7", "8", "7", "8", "7", "8", "9", "8", "9", "8", "9", "8", "9", "8", "9", "10", "9", "10", "9", "10", "9", "10", "9", "10", "9", "10", "11", "10", "11", "10", "11", "10", "11", "10", "11", "10", "11", "10", "11", "12" ]
[ "nonn" ]
18
0
3
[ "A277281", "A381524", "A381737" ]
null
Mike Sheppard, Feb 26 2025
2025-03-18T07:22:26
oeisdata/seq/A381/A381524.seq
dab65b9f18f5ec15274095b58aa59c3a
A381525
Squarefree semiprimes k = p*q, primes p < q, with q distinct power residues r (mod k) congruent to p^m, m >= 0, and p distinct power residues r (mod k) congruent to q^m, m >= 0.
[ "6", "10", "15", "22", "26", "35", "38", "51", "58", "74", "85", "87", "106", "115", "118", "119", "122", "134", "143", "159", "166", "185", "187", "202", "214", "215", "235", "247", "262", "265", "267", "278", "298", "303", "319", "326", "339", "346", "358", "362", "365", "391", "394", "411", "415", "422", "427", "447", "451", "454", "481", "485", "515", "519", "527" ]
[ "nonn", "easy" ]
33
1
1
[ "A006881", "A007947", "A381525", "A381804" ]
null
Michael De Vlieger, Mar 24 2025
2025-03-29T18:17:28
oeisdata/seq/A381/A381525.seq
aef00f8cca470080ae7a1c6724472366
A381526
a(n) is the smallest positive integer k such that the decimal expansion of k is a substring of the decimal expansion of n*k, or -1 if no such number exists.
[ "-1", "1", "-1", "5", "-1", "5", "2", "5", "-1", "5", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "-1", "1", "9", "5", "72", "5", "2", "5", "6", "5", "5", "1", "91", "5", "42", "4", "2", "4", "36", "5", "-1", "1", "94", "5", "3", "3", "2", "5", "8", "5", "5", "1", "24", "5", "7", "5", "2", "5", "21", "5", "2", "1", "2", "2", "2", "5", "2", "5", "7", "5", "5", "1", "484", "5", "47", "5", "2", "3", "3", "3", "-1" ]
[ "sign", "base", "easy", "look" ]
16
0
4
[ "A239134", "A337084", "A381526", "A381527", "A381528" ]
null
Dominic McCarty, Feb 26 2025
2025-03-03T13:36:48
oeisdata/seq/A381/A381526.seq
5e9004502000924837de9d323f0cd8f1
A381527
a(n) is the smallest positive multiple of n such that the decimal expansion of a(n)/n is a substring of the decimal expansion of a(n), or -1 if no such number exists.
[ "-1", "1", "-1", "15", "-1", "25", "12", "35", "-1", "45", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "-1", "21", "198", "115", "1728", "125", "52", "135", "168", "145", "150", "31", "2912", "165", "1428", "140", "72", "148", "1368", "195", "-1", "41", "3948", "215", "132", "135", "92", "235", "384", "245", "250", "51", "1248", "265", "378", "275" ]
[ "sign", "easy" ]
10
0
4
[ "A381526", "A381527" ]
null
Dominic McCarty, Feb 26 2025
2025-03-03T13:37:09
oeisdata/seq/A381/A381527.seq
509c34cf7eaf3d4be8c94452474e584d
A381528
Indices of records in A381526.
[ "0", "1", "3", "22", "24", "32", "42", "72", "84", "384", "724", "2584", "200000002", "200000004", "2000000002" ]
[ "nonn" ]
6
1
3
[ "A381526", "A381528" ]
null
Dominic McCarty, Feb 26 2025
2025-03-03T13:37:19
oeisdata/seq/A381/A381528.seq
7bcd06fa6d67b6e2c95e0616c38cc11d