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1999-12-11 03:00:00
2025-04-25 01:21:50
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A360001
Expansion of Product_{k>=0} (1 - x^(k^2+4)) in powers of x.
[ "1", "0", "0", "0", "-1", "-1", "0", "0", "-1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "-1", "1", "-1", "0", "1", "0", "-1", "0", "1", "-2", "1", "0", "-1", "1", "1", "0", "0", "1", "-2", "0", "-1", "-2", "1", "0", "1", "2", "1", "-1", "1", "0", "-2", "1", "-1", "-2", "0", "1", "0", "0", "1", "-1", "1", "1", "0", "0", "-1", "-1", "1", "1", "-2", "2", "0", "-2", "2", "1", "-3", "0", "1", "-3", "2", "2", "-1", "1" ]
[ "sign", "look" ]
10
0
5
[ "A276516", "A359936", "A359966", "A359980", "A360001", "A360002", "A360003" ]
null
Seiichi Manyama, Jan 21 2023
2023-01-21T11:51:43
oeisdata/seq/A360/A360001.seq
63e9bce76a4340a07f48da1a069273af
A360002
Expansion of Product_{k>=0} (1 - x^(k^2+5)) in powers of x.
[ "1", "0", "0", "0", "0", "-1", "-1", "0", "0", "-1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "-1", "0", "1", "0", "-1", "1", "1", "-1", "-1", "0", "0", "-1", "0", "1", "1", "0", "0", "0", "1", "-1", "-2", "0", "0", "-1", "-1", "2", "1", "0", "0", "2", "1", "-1", "-1", "-1", "0", "-2", "-1", "1", "2", "-1", "0", "2", "1", "-2", "-1", "2", "-1", "-1", "-1", "2", "0", "0", "0", "2", "1", "-2", "-1", "1", "0", "-4", "0", "2" ]
[ "sign", "look" ]
11
0
5
[ "A276516", "A359936", "A359966", "A359980", "A360001", "A360002", "A360003" ]
null
Seiichi Manyama, Jan 21 2023
2023-01-21T11:51:40
oeisdata/seq/A360/A360002.seq
c975f9e823b12dfab73575df9000eb8b
A360003
Expansion of Product_{k>=0} (1 - x^(k^2+10)) in powers of x.
[ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "0", "0", "-1", "0", "0", "0", "0", "-1", "0", "1", "0", "0", "1", "1", "-1", "0", "0", "1", "1", "0", "0", "1", "0", "-2", "1", "1", "0", "0", "0", "0", "0", "-1", "-1", "2", "0", "-1", "0", "1", "-1", "-1", "0", "0", "2", "-1", "-1", "1", "0", "-3", "0", "2", "0", "0", "-1", "0", "1", "-1", "-1", "2", "2", "-2", "0", "1", "-1", "-1", "-1", "0", "2", "0", "-3", "2", "0", "-2" ]
[ "sign", "look" ]
11
0
5
[ "A276516", "A359936", "A359966", "A359980", "A360001", "A360002", "A360003" ]
null
Seiichi Manyama, Jan 21 2023
2023-01-21T11:51:37
oeisdata/seq/A360/A360003.seq
940e63ff998eb6955424428c453e874c
A360004
Sequence of composite digits as they appear in Pi.
[ "4", "9", "6", "8", "9", "9", "8", "4", "6", "6", "4", "8", "9", "8", "8", "4", "9", "6", "9", "9", "9", "8", "9", "4", "9", "4", "4", "9", "8", "6", "4", "6", "8", "6", "8", "9", "9", "8", "6", "8", "4", "8", "4", "6", "9", "8", "4", "8", "8", "6", "8", "6", "6", "4", "9", "8", "4", "4", "6", "9", "8", "9", "4", "8", "8", "4", "8", "4", "8", "4", "9", "8", "9", "6", "4", "4", "6", "9", "4", "8", "9", "4", "9", "8", "9", "6", "4", "4", "8", "8", "9", "6", "6", "9", "4", "4", "6", "8", "4" ]
[ "nonn", "base", "easy" ]
39
0
5
[ "A000796", "A002808", "A073264", "A086385", "A086399", "A360004" ]
null
Miles Galvin, Jan 21 2023
2023-03-10T19:39:10
oeisdata/seq/A360/A360004.seq
19ea194b6bd1cf9555fdfbf3b933c495
A360005
Two times the median of the multiset of prime indices of n.
[ "2", "4", "2", "6", "3", "8", "2", "4", "4", "10", "2", "12", "5", "5", "2", "14", "4", "16", "2", "6", "6", "18", "2", "6", "7", "4", "2", "20", "4", "22", "2", "7", "8", "7", "3", "24", "9", "8", "2", "26", "4", "28", "2", "4", "10", "30", "2", "8", "6", "9", "2", "32", "4", "8", "2", "10", "11", "34", "3", "36", "12", "4", "2", "9", "4", "38", "2", "11", "6", "40", "2", "42", "13", "6", "2", "9", "4", "44", "2" ]
[ "nonn" ]
6
0
5
[ "A001222", "A026424", "A056239", "A112798", "A307683", "A316413", "A325347", "A326567", "A326568", "A359889", "A359890", "A359893", "A359901", "A359902", "A359907", "A359908", "A359912", "A360005", "A360006", "A360007", "A360009" ]
null
Gus Wiseman, Jan 23 2023
2023-01-23T12:41:26
oeisdata/seq/A360/A360005.seq
602e1e413dca6b9c70ef27379c761db0
A360006
Least positive integer whose prime indices have median n/2. a(1) = 1.
[ "1", "2", "6", "3", "14", "5", "26", "7", "38", "11", "58", "13", "74", "17", "86", "19", "106", "23", "122", "29", "142", "31", "158", "37", "178", "41", "202", "43", "214", "47", "226", "53", "262", "59", "278", "61", "302", "67", "326", "71", "346", "73", "362", "79", "386", "83", "398", "89", "446", "97", "458", "101", "478", "103", "502", "107", "526", "109", "542", "113" ]
[ "nonn" ]
5
0
5
[ "A001222", "A026424", "A056239", "A112798", "A307683", "A316413", "A325347", "A326567", "A326568", "A359889", "A359890", "A359893", "A359901", "A359902", "A359907", "A359908", "A359912", "A360005", "A360006", "A360007", "A360008", "A360009" ]
null
Gus Wiseman, Jan 24 2023
2023-01-24T12:35:47
oeisdata/seq/A360/A360006.seq
9bcdc29fda3475ef077401fee135fc17
A360007
Positions of first appearances in the sequence giving the median of the prime indices of n (A360005(n)/2).
[ "1", "2", "3", "5", "6", "7", "11", "13", "14", "17", "19", "23", "26", "29", "31", "37", "38", "41", "43", "47", "53", "58", "59", "61", "67", "71", "73", "74", "79", "83", "86", "89", "97", "101", "103", "106", "107", "109", "113", "122", "127", "131", "137", "139", "142", "149", "151", "157", "158", "163", "167", "173", "178", "179", "181", "191", "193", "197", "199", "202" ]
[ "nonn" ]
5
0
5
[ "A001222", "A026424", "A056239", "A112798", "A307683", "A316413", "A325347", "A326567", "A326568", "A359889", "A359890", "A359893", "A359901", "A359902", "A359907", "A359908", "A359912", "A360005", "A360006", "A360007", "A360008", "A360009" ]
null
Gus Wiseman, Jan 24 2023
2023-01-24T12:35:41
oeisdata/seq/A360/A360007.seq
0197556dedbb155c185bd957e648f4fc
A360008
Positions of first appearances in the sequence giving the mean of prime indices (A326567/A326568).
[ "1", "3", "5", "6", "7", "11", "12", "13", "14", "17", "18", "19", "23", "24", "26", "29", "31", "37", "38", "41", "42", "43", "47", "48", "52", "53", "54", "58", "59", "61", "67", "71", "72", "73", "74", "76", "79", "83", "86", "89", "92", "96", "97", "101", "103", "104", "106", "107", "108", "109", "113", "122", "124", "127", "131", "137", "139", "142", "148", "149", "151", "152" ]
[ "nonn" ]
6
0
5
[ "A001222", "A008284", "A026424", "A051293", "A056239", "A058398", "A112798", "A316413", "A326567", "A326568", "A327473", "A327482", "A348551", "A359889", "A359908", "A359912", "A360005", "A360006", "A360007", "A360008" ]
null
Gus Wiseman, Jan 24 2023
2023-01-24T12:35:36
oeisdata/seq/A360/A360008.seq
84770fd55b1cbef67334db6871881013
A360009
Numbers whose prime indices have integer mean and integer median.
[ "2", "3", "4", "5", "7", "8", "9", "10", "11", "13", "16", "17", "19", "21", "22", "23", "25", "27", "28", "29", "30", "31", "32", "34", "37", "39", "41", "43", "46", "47", "49", "53", "55", "57", "59", "61", "62", "64", "67", "68", "71", "73", "78", "79", "81", "82", "83", "85", "87", "88", "89", "90", "91", "94", "97", "98", "99", "100", "101", "103", "105", "107", "109", "110", "111" ]
[ "nonn" ]
6
0
5
[ "A001222", "A008284", "A026424", "A056239", "A058398", "A067538", "A112798", "A307683", "A316413", "A325347", "A326567", "A326568", "A326622", "A327473", "A327482", "A328966", "A348551", "A349156", "A359889", "A359890", "A359893", "A359901", "A359902", "A359903", "A359905", "A359906", "A359908", "A359912", "A360005", "A360006", "A360009" ]
null
Gus Wiseman, Jan 24 2023
2023-01-24T12:35:30
oeisdata/seq/A360/A360009.seq
175ad838ef8655fd317809fd4d868405
A360010
First part of the n-th weakly decreasing triple of positive integers sorted lexicographically. Each n > 0 is repeated A000217(n) times.
[ "1", "2", "2", "2", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8" ]
[ "nonn" ]
12
0
5
[ "A000217", "A000292", "A002024", "A003056", "A050407", "A056556", "A056557", "A056558", "A069905", "A070770", "A158842", "A194848", "A331195", "A333516", "A360010", "A360240" ]
null
Gus Wiseman, Feb 11 2023
2024-11-05T12:19:11
oeisdata/seq/A360/A360010.seq
889412ecc4379856607abd138880561f
A360011
Integers k such that the product of the first k primes is a Niven number.
[ "0", "1", "2", "3", "4", "5", "6", "9", "11", "13", "14", "15", "16", "18", "19", "21", "22", "27", "28", "30", "31", "32", "34", "35", "36", "38", "39", "46", "47", "49", "50", "52", "54", "55", "57", "58", "60", "61", "62", "63", "64", "65", "66", "69", "70", "74", "75", "77", "78", "79", "80", "82", "83", "84", "85", "86", "87", "88", "90", "91", "92", "93", "94", "95", "96", "97", "98", "99", "100" ]
[ "nonn", "base" ]
17
0
5
[ "A002110", "A005349", "A359960", "A360011" ]
null
Michel Marcus, Jan 21 2023
2023-01-21T09:33:20
oeisdata/seq/A360/A360011.seq
6284f2e72c672a087f976c0d065a4419
A360012
a(n) is the number of triples (u,v,w) of divisors of n with u/v = v/w, and u < v < w.
[ "0", "0", "0", "1", "0", "0", "0", "2", "1", "0", "0", "2", "0", "0", "0", "4", "0", "2", "0", "2", "0", "0", "0", "4", "1", "0", "2", "2", "0", "0", "0", "6", "0", "0", "0", "8", "0", "0", "0", "4", "0", "0", "0", "2", "2", "0", "0", "8", "1", "2", "0", "2", "0", "4", "0", "4", "0", "0", "0", "4", "0", "0", "2", "9", "0", "0", "0", "2", "0", "0", "0", "14", "0", "0", "2", "2", "0", "0", "0", "8", "4", "0", "0", "4", "0", "0", "0" ]
[ "nonn" ]
8
0
5
[ "A002620", "A005059", "A091009", "A132345", "A360012" ]
null
Rémy Sigrist, Jan 21 2023
2023-01-22T16:02:36
oeisdata/seq/A360/A360012.seq
93f01d5f2500b80df24821b75d158f9d
A360013
Numbers whose exponent of 2 in their canonical prime factorization is larger than all the other exponents.
[ "2", "4", "8", "12", "16", "20", "24", "28", "32", "40", "44", "48", "52", "56", "60", "64", "68", "72", "76", "80", "84", "88", "92", "96", "104", "112", "116", "120", "124", "128", "132", "136", "140", "144", "148", "152", "156", "160", "164", "168", "172", "176", "184", "188", "192", "200", "204", "208", "212", "220", "224", "228", "232", "236", "240", "244", "248", "256" ]
[ "nonn", "easy" ]
45
0
5
[ "A000079", "A000265", "A001222", "A002865", "A007814", "A051903", "A056911", "A118914", "A124010", "A241131", "A327473", "A327476", "A335738", "A356862", "A359178", "A360013", "A360014", "A360015", "A362605", "A362606", "A362608", "A362610", "A362611", "A362612", "A362613", "A362614", "A362615", "A362616", "A363486", "A363487", "A363723", "A363727", "A364061", "A364062", "A364160", "A364193" ]
null
Amiram Eldar, Jan 21 2023
2024-07-17T09:58:51
oeisdata/seq/A360/A360013.seq
c3498830a2285dfb887fff768c914d57
A360014
Numbers whose exponent of 2 in their canonical prime factorization is equal to the maximum of the other exponents.
[ "1", "6", "10", "14", "22", "26", "30", "34", "36", "38", "42", "46", "58", "62", "66", "70", "74", "78", "82", "86", "94", "100", "102", "106", "110", "114", "118", "122", "130", "134", "138", "142", "146", "154", "158", "166", "170", "174", "178", "180", "182", "186", "190", "194", "196", "202", "206", "210", "214", "216", "218", "222", "226", "230", "238", "246", "252" ]
[ "nonn", "easy" ]
9
0
5
[ "A000265", "A007814", "A039956", "A051903", "A067259", "A360013", "A360014", "A360015" ]
null
Amiram Eldar, Jan 21 2023
2023-01-23T02:33:02
oeisdata/seq/A360/A360014.seq
59f3581045f249e5961dc299ec6c6411
A360015
Numbers whose exponent of 2 in their canonical prime factorization is equal to the maximal exponent.
[ "1", "2", "4", "6", "8", "10", "12", "14", "16", "20", "22", "24", "26", "28", "30", "32", "34", "36", "38", "40", "42", "44", "46", "48", "52", "56", "58", "60", "62", "64", "66", "68", "70", "72", "74", "76", "78", "80", "82", "84", "86", "88", "92", "94", "96", "100", "102", "104", "106", "110", "112", "114", "116", "118", "120", "122", "124", "128", "130", "132", "134", "136", "138" ]
[ "nonn", "easy" ]
28
0
5
[ "A000079", "A000265", "A001222", "A002865", "A007814", "A027746", "A051903", "A056239", "A056911", "A112798", "A241131", "A327473", "A327476", "A356862", "A359178", "A360013", "A360014", "A360015", "A362605", "A362611", "A362613", "A362614", "A363486", "A364061", "A364062", "A364158", "A364159" ]
null
Amiram Eldar, Jan 21 2023
2023-07-30T01:35:13
oeisdata/seq/A360/A360015.seq
b608505ab0f99526cf46c5cacff3cec5
A360016
Number of partitions of 4*n into four odd primes (p_1, p_2, p_3, p_4) (p_1 < p_2 <= p_3 < p_4 and p_1 + p_4 = p_2 + p_3 = 2*n) such that (p_1, p_2) and (p_3, p_4) are consecutive pairs of prime numbers with the same difference, d = p_2 - p_1 = p_4 - p_3, and (p_1, p_3), (p_2, p_4) are also consecutive pairs of prime numbers with the same difference, D = p_3 - p_1 = p_4 - p_2.
[ "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "3", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "2", "0", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "3", "0" ]
[ "nonn", "easy" ]
34
0
5
[ "A001359", "A006512", "A023200", "A023201", "A046117", "A046132", "A360016" ]
null
Naohiro Nomoto, Jan 21 2023
2023-02-16T05:29:06
oeisdata/seq/A360/A360016.seq
ed7f5919fd8af9fca12590560ea61107
A360017
Nonsquarefree numbers k such that k - d is also a nonsquarefree number for all proper divisors d of k.
[ "25", "50", "125", "169", "243", "289", "325", "343", "351", "361", "425", "605", "625", "725", "729", "841", "845", "925", "1025", "1053", "1325", "1369", "1445", "1450", "1525", "1625", "1681", "1825", "1850", "2125", "2197", "2225", "2401", "2425", "2525", "2725", "2809", "2825", "2873", "3125", "3425", "3625", "3721", "3725", "3757", "3872", "3925", "4205", "4225", "4325", "4525" ]
[ "nonn" ]
26
0
5
[ "A013929", "A027751", "A360017" ]
null
Juri-Stepan Gerasimov, Jan 21 2023
2023-02-11T20:31:47
oeisdata/seq/A360/A360017.seq
1533c0fa6981d3e694794a3fcaa44bb2
A360018
Expansion of Sum_{k>=0} (k * x * (1 + (k * x)^2))^k.
[ "1", "1", "4", "28", "288", "3854", "63104", "1220729", "27248128", "689446671", "19501121536", "609753349945", "20883798220800", "777529328875208", "31266494467227648", "1350520199148276667", "62360172065142341632", "3065369553470816704832", "159818389764050045894656" ]
[ "nonn" ]
26
0
5
[ "A360018", "A360032", "A360618", "A360730" ]
null
Seiichi Manyama, Feb 19 2023
2023-02-20T06:13:39
oeisdata/seq/A360/A360018.seq
67c89f3b22b9c41ea95ffb14e5094ddc
A360019
Lexicographically earliest increasing sequence of positive numbers in which no nonempty subsequence of consecutive terms sums to a triangular number.
[ "2", "5", "7", "11", "12", "14", "16", "17", "18", "19", "20", "22", "25", "26", "30", "31", "34", "35", "37", "42", "46", "49", "52", "54", "59", "63", "64", "68", "72", "73", "77", "80", "81", "84", "85", "87", "92", "93", "94", "98", "100", "101", "108", "113", "115", "117", "118", "121", "122", "123", "125", "129", "130", "132", "133", "134", "141", "142", "143", "146", "149" ]
[ "nonn" ]
35
0
5
[ "A000217", "A084833", "A332941", "A360019" ]
null
Ctibor O. Zizka, Jan 21 2023
2023-01-22T17:48:05
oeisdata/seq/A360/A360019.seq
ebc4c69d1f894e4ae59c8d6ccac908f8
A360020
Irregular triangle T(n, k), n > 0, k = 1..A056137(A009023(n)), read by rows: T(n, k) is the square root of A009023(n)^2 + A359805(n, k)^2.
[ "5", "10", "13", "15", "17", "20", "25", "29", "25", "26", "30", "35", "34", "40", "37", "39", "45", "41", "50", "58", "55", "51", "53", "50", "52", "60", "65", "73", "65", "70", "61", "65", "68", "75", "65", "87", "80", "85", "74", "75", "78", "90", "97", "85", "95", "85", "82", "89", "100", "85", "91", "105", "116", "110", "102", "106", "109", "115", "100", "104", "120", "101" ]
[ "nonn", "look", "tabf" ]
13
0
5
[ "A000196", "A009023", "A056137", "A359805", "A360020" ]
null
Rémy Sigrist, Mar 08 2023
2023-03-13T05:52:07
oeisdata/seq/A360/A360020.seq
77b0625378c6e501b1ba1828a9c7921e
A360021
Number of unordered triples of self-avoiding paths with nodes that cover all vertices of a convex n-gon; one-node paths are allowed.
[ "1", "6", "45", "315", "2205", "15624", "111888", "807840", "5868720", "42799680", "312504192", "2278418688", "16549827840", "119567831040", "858293084160", "6118081708032", "43298650386432", "304260332175360", "2123395686236160", "14722247331348480", "101446590051975168", "695007859780878336", "4735844958575001600" ]
[ "nonn", "easy" ]
17
0
5
[ "A359405", "A360021" ]
null
Ivaylo Kortezov, Jan 22 2023
2023-02-11T20:31:58
oeisdata/seq/A360/A360021.seq
94004db8e724a9bc6bfa45469ef971b6
A360022
Triangle read by rows: T(n,k) is the sum of the widths of the k-th diagonals of the symmetric representation of sigma(n).
[ "1", "1", "2", "0", "2", "2", "1", "2", "2", "2", "0", "0", "2", "2", "2", "2", "2", "2", "2", "2", "2", "0", "0", "0", "2", "2", "2", "2", "1", "2", "2", "2", "2", "2", "2", "2", "1", "2", "0", "0", "2", "2", "2", "2", "2", "0", "2", "2", "2", "2", "2", "2", "2", "2", "2", "0", "0", "0", "0", "0", "2", "2", "2", "2", "2", "2", "2", "4", "4", "2", "2", "2", "2", "2", "2", "2", "2", "2", "0", "0", "0", "0", "0", "0", "2", "2", "2", "2", "2", "2", "2", "0", "0", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2" ]
[ "nonn", "tabl" ]
37
0
5
[ "A000079", "A000203", "A000396", "A007395", "A040000", "A065091", "A067742", "A196020", "A235791", "A236104", "A237270", "A237271", "A237591", "A237593", "A245092", "A249351", "A250068", "A250070", "A262626", "A360022" ]
null
Omar E. Pol, Jan 22 2023
2023-02-05T13:49:16
oeisdata/seq/A360/A360022.seq
518068c629c5284c1088ab3b7f39ebf8
A360023
Expansion of e.g.f. x*exp(x)*(cosh(x))^2.
[ "0", "1", "2", "9", "28", "105", "366", "1281", "4376", "14769", "49210", "162393", "531444", "1727193", "5580134", "17936145", "57395632", "182948577", "581130738", "1840247337", "5811307340", "18305618121", "57531942622", "180441092769", "564859072968", "1765184603025", "5507375961386", "17157594341241", "53379182394916", "165856745298489" ]
[ "nonn", "easy" ]
41
0
5
[ "A122983", "A360023", "A360035", "A360036" ]
null
Enrique Navarrete, Jan 22 2023
2023-02-20T14:51:17
oeisdata/seq/A360/A360023.seq
e7632bf7e418c3e320ff7c888be73c5b
A360024
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n-k,k) * Catalan(k).
[ "1", "1", "0", "-1", "0", "3", "3", "-5", "-12", "5", "41", "21", "-110", "-165", "210", "735", "-30", "-2505", "-2205", "6555", "13710", "-10035", "-57390", "-18471", "185790", "240793", "-436317", "-1276795", "360302", "4956495", "3410749", "-14776581", "-26548200", "28671609", "124807175", "14211153", "-446256722", "-481156685" ]
[ "sign" ]
21
0
5
[ "A000108", "A360024", "A360025", "A360026", "A360027" ]
null
Seiichi Manyama, Jan 22 2023
2023-01-25T08:21:59
oeisdata/seq/A360/A360024.seq
89e6f7638885682c31e2629aba7a55a1
A360025
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-2*k,k) * Catalan(k).
[ "1", "1", "1", "0", "-1", "-2", "-1", "2", "7", "9", "3", "-16", "-39", "-43", "9", "126", "247", "199", "-213", "-984", "-1555", "-756", "2525", "7518", "9593", "559", "-24899", "-56216", "-55241", "33150", "225879", "407194", "273199", "-529745", "-1938549", "-2822128", "-833219", "6083986", "15904733", "18288966", "-4172187", "-61154333" ]
[ "sign" ]
24
0
5
[ "A000108", "A216604", "A349047", "A360024", "A360025", "A360026", "A360027" ]
null
Seiichi Manyama, Jan 22 2023
2023-01-25T08:23:55
oeisdata/seq/A360/A360025.seq
d075f75d0ce361461d641d850a51cb5a
A360026
a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k) * Catalan(k).
[ "1", "1", "1", "1", "0", "-1", "-2", "-3", "-2", "1", "6", "13", "17", "13", "-4", "-39", "-83", "-113", "-92", "31", "279", "605", "850", "701", "-219", "-2129", "-4736", "-6749", "-5690", "1569", "17114", "38713", "55957", "48249", "-11498", "-142163", "-326860", "-478957", "-421262", "84015", "1210831", "2829363", "4197670", "3762583", "-601732" ]
[ "sign" ]
23
0
5
[ "A000108", "A346073", "A349048", "A360024", "A360025", "A360026", "A360027" ]
null
Seiichi Manyama, Jan 22 2023
2023-01-25T08:25:34
oeisdata/seq/A360/A360026.seq
52d5c76347c0708267562b78d32ad459
A360027
a(n) = Sum_{k=0..floor(n/5)} (-1)^k * binomial(n-4*k,k) * Catalan(k).
[ "1", "1", "1", "1", "1", "0", "-1", "-2", "-3", "-4", "-3", "0", "5", "12", "21", "27", "25", "10", "-23", "-79", "-149", "-210", "-225", "-143", "101", "544", "1153", "1783", "2135", "1714", "-81", "-3735", "-9263", "-15724", "-20603", "-19490", "-6485", "24242", "75307", "140955", "200891", "215530", "126527", "-132122", "-605687" ]
[ "sign" ]
24
0
5
[ "A000108", "A346074", "A360024", "A360025", "A360026", "A360027" ]
null
Seiichi Manyama, Jan 22 2023
2023-01-25T08:27:44
oeisdata/seq/A360/A360027.seq
4b258e6677e3948d7bdf4c445adde214
A360028
Lexicographically earliest sequence of positive numbers in which no nonempty subsequence of consecutive terms sums to a semiprime.
[ "1", "1", "1", "16", "1", "11", "1", "11", "30", "30", "79", "17", "44", "28", "12", "30", "150", "144", "252", "304", "20", "300", "132", "12", "252", "234", "18", "112", "32", "456", "52", "520", "60", "28", "120", "180", "162", "2", "52", "324", "42", "130", "20", "60", "100", "92", "132", "126", "186", "184", "104", "12", "104", "320", "8", "12", "20", "320", "104", "16", "32", "208", "404", "240", "300", "60", "408" ]
[ "nonn" ]
20
0
5
[ "A001358", "A332941", "A360028" ]
null
Ctibor O. Zizka, Jan 22 2023
2023-02-15T14:03:32
oeisdata/seq/A360/A360028.seq
c5f00713b25894093927adaa701c5984
A360029
Consider a ruler composed of n segments with lengths 1, 1/2, 1/3, ..., 1/n with total length A001008(n)/A002805(n). a(n) is the minimum number of distinct distances of all pairs of marks that can be achieved by permuting the positions of the segments.
[ "1", "3", "6", "10", "15", "18", "25", "33", "42", "52", "63", "71", "84", "98", "107", "123", "140", "152", "171", "185", "198", "220", "243", "256", "281", "307", "334", "354", "383", "403", "434", "466", "489", "523", "552", "581", "618", "656", "695", "728" ]
[ "nonn", "hard", "more" ]
25
0
5
[ "A000217", "A001008", "A002805", "A003022", "A360029" ]
null
Hugo Pfoertner, Jan 22 2023
2023-02-19T09:17:12
oeisdata/seq/A360/A360029.seq
cda8d2f727971d262a07f060a1ad449b
A360030
a(n) is the minimum number of equal resistors needed in an electrical network so that n nodes can be selected in this network such that there are n*(n-1)/2 distinct resistances 0 < R < oo between the selected nodes.
[ "1", "3", "5", "8", "10", "11", "12" ]
[ "nonn", "more" ]
9
0
5
[ "A219158", "A342558", "A348020", "A360030" ]
null
Hugo Pfoertner and Rainer Rosenthal, Feb 12 2023
2023-02-18T08:08:25
oeisdata/seq/A360/A360030.seq
b918a5bc083754a16550f21b576718af
A360031
a(n) is the number of unlabeled 2-connected graphs with n edges containing at least one pair of nodes with resistance distance 1 when all edges are replaced by unit resistors.
[ "0", "1", "1", "1", "2", "5", "14", "35", "111", "341", "1130", "3969", "15002", "58429", "239045", "1012241" ]
[ "nonn", "more" ]
6
0
5
[ "A010355", "A339070", "A342558", "A360030", "A360031" ]
null
Hugo Pfoertner, Mar 11 2023
2023-03-31T09:17:34
oeisdata/seq/A360/A360031.seq
00df85122c8347889d269cd22f8bd5c5
A360032
Expansion of Sum_{k>=0} (k * x * (1 + (k * x)^3))^k.
[ "1", "1", "4", "27", "257", "3189", "48843", "889079", "18730597", "447945714", "11983618199", "354519428597", "11490618543066", "404910044246256", "15412461332440829", "630199633730994675", "27548323149955792880", "1282044807268698303751", "63284535745130267484867" ]
[ "nonn" ]
19
0
5
[ "A360018", "A360032", "A360618", "A360731" ]
null
Seiichi Manyama, Feb 19 2023
2023-02-19T09:21:09
oeisdata/seq/A360/A360032.seq
9a0b33e14d09bb51302c98d8acf2e6c3
A360033
Table T(n,k), n >= 1 and k >= 0, read by antidiagonals, related to Jacobsthal numbers A001045.
[ "1", "2", "1", "3", "3", "3", "4", "5", "7", "5", "5", "7", "11", "13", "11", "6", "9", "15", "21", "27", "21", "7", "11", "19", "29", "43", "53", "43", "8", "13", "23", "37", "59", "85", "107", "85", "9", "15", "27", "45", "75", "117", "171", "213", "171", "10", "17", "31", "53", "91", "149", "235", "341", "427", "341", "11", "19", "35", "61", "107", "181", "299", "469" ]
[ "nonn", "tabl", "easy" ]
11
0
5
[ "A000027", "A001045", "A004767", "A004770", "A005408", "A048573", "A062092", "A106839", "A360033" ]
null
Philippe Deléham, Jan 22 2023
2023-02-04T11:10:11
oeisdata/seq/A360/A360033.seq
248fd11d62b2f50cd837101673efad31
A360034
Binary representation of -n in base i-1.
[ "0", "11101", "11100", "10001", "10000", "11001101", "11001100", "11000001", "11000000", "11011101", "11011100", "11010001", "11010000", "1110100001101", "1110100001100", "1110100000001", "1110100000000", "1110100011101", "1110100011100", "1110100010001", "1110100010000", "1110111001101", "1110111001100", "1110111000001" ]
[ "nonn", "base", "easy" ]
16
0
5
[ "A256441", "A271472", "A360034" ]
null
Jianing Song, Jan 22 2023
2023-01-23T16:18:14
oeisdata/seq/A360/A360034.seq
2ceeeafe84b7e73c7db6ebc6cf064caf
A360035
Expansion of e.g.f. x*exp(x)*cosh(x)*sinh(x).
[ "0", "0", "2", "6", "28", "100", "366", "1274", "4376", "14760", "49210", "162382", "531444", "1727180", "5580134", "17936130", "57395632", "182948560", "581130738", "1840247318", "5811307340", "18305618100", "57531942622", "180441092746", "564859072968", "1765184603000", "5507375961386", "17157594341214", "53379182394916" ]
[ "nonn", "easy" ]
27
0
5
[ "A015518", "A360023", "A360035", "A360036" ]
null
Enrique Navarrete, Jan 22 2023
2023-02-12T15:19:11
oeisdata/seq/A360/A360035.seq
2ef48a64591f803f2dff193c66c5efcf
A360036
Expansion of e.g.f. x*exp(x)*(sinh(x))^2.
[ "0", "0", "0", "6", "24", "100", "360", "1274", "4368", "14760", "49200", "162382", "531432", "1727180", "5580120", "17936130", "57395616", "182948560", "581130720", "1840247318", "5811307320", "18305618100", "57531942600", "180441092746", "564859072944", "1765184603000", "5507375961360", "17157594341214", "53379182394888" ]
[ "nonn", "easy" ]
25
0
5
[ "A015518", "A081251", "A360023", "A360035", "A360036" ]
null
Enrique Navarrete, Jan 22 2023
2023-02-12T15:19:02
oeisdata/seq/A360/A360036.seq
6ec567a7de0df38d7dffb575a85577aa
A360037
Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 2, 2, 2, ..., n, n, n] into k nonempty subsets, for 3 <= k <= 3n.
[ "1", "1", "1", "1", "1", "1", "4", "10", "13", "7", "3", "1", "1", "14", "92", "221", "249", "172", "81", "25", "6", "1", "1", "50", "872", "4277", "8806", "9840", "6945", "3377", "1206", "325", "65", "10", "1", "1", "186", "8496", "85941", "320320", "585960", "627838", "442321", "221475", "82985", "24038", "5496", "995", "140", "15", "1" ]
[ "nonn", "tabf" ]
28
0
5
[ "A098233", "A165434", "A360037", "A360038", "A360039" ]
null
Marko Riedel, Jan 22 2023
2023-05-07T04:10:10
oeisdata/seq/A360/A360037.seq
3e84c518fc28463675b81230ed136040
A360038
Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 2, 2, 2, 2, ..., n, n, n, n] into k nonempty subsets, for 4 <= k <= 4n.
[ "1", "1", "1", "1", "1", "1", "1", "4", "11", "19", "22", "13", "7", "3", "1", "1", "14", "117", "445", "873", "1002", "805", "483", "226", "81", "25", "6", "1", "1", "51", "1387", "12567", "47986", "96620", "120970", "104942", "67901", "34385", "14150", "4817", "1371", "325", "65", "10", "1", "1", "201", "18171", "396571", "3053216", "11003801", "22360580", "29114463", "26607981", "18227245", "9816458", "4301588", "1572206", "487670", "129880", "29828", "5901", "995", "140", "15", "1" ]
[ "nonn", "tabf" ]
15
0
5
[ "A098233", "A165435", "A360037", "A360038", "A360039" ]
null
Marko Riedel, Jan 22 2023
2023-01-25T16:26:47
oeisdata/seq/A360/A360038.seq
8e41f3872d1f6dd9c1bd17abe5e3799c
A360039
Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, ..., n, n, n, n, n] into k nonempty subsets, for 5 <= k <= 5n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "4", "11", "22", "32", "34", "22", "13", "7", "3", "1", "1", "14", "123", "611", "1703", "2916", "3371", "2935", "2046", "1171", "561", "226", "81", "25", "6", "1", "1", "51", "1622", "22172", "134766", "430780", "838335", "1110757", "1086681", "831650", "519000", "272212", "122736", "48255", "16670", "5087", "1371", "325", "65", "10", "1", "1", "202", "25223", "975478", "13471057", "84718407", "290637504", "619325134" ]
[ "nonn", "tabf" ]
15
0
5
[ "A098233", "A165436", "A360037", "A360038", "A360039" ]
null
Marko Riedel, Jan 22 2023
2023-01-25T16:26:42
oeisdata/seq/A360/A360039.seq
a8efa31d473c52f2ae4c692ca261f015
A360040
Prime numbers missing from A359136: prime numbers for which none of the nontrivial permutations of its digits (permitting leading zeros) produces a prime number.
[ "2", "3", "5", "7", "19", "23", "29", "41", "43", "47", "53", "59", "61", "67", "83", "89", "257", "263", "269", "409", "431", "487", "523", "541", "827", "829", "853", "859", "2861", "4027", "4801", "5209", "5623", "5849" ]
[ "nonn", "base", "fini", "full" ]
10
0
5
[ "A359136", "A359137", "A360040", "A360041" ]
null
Rémy Sigrist, Jan 23 2023
2023-01-23T09:10:19
oeisdata/seq/A360/A360040.seq
32470a301009d7129052d5933db708d1
A360041
Prime numbers missing from A359137: prime numbers for which none of the nontrivial permutations of its digits (not permitting leading zeros) produces a prime number.
[ "2", "3", "5", "7", "19", "23", "29", "41", "43", "47", "53", "59", "61", "67", "83", "89", "103", "109", "257", "263", "269", "307", "401", "409", "431", "487", "503", "509", "523", "541", "601", "607", "809", "827", "829", "853", "859", "2017", "2087", "2861", "4027", "4051", "4079", "4801", "5021", "5209", "5623", "5849", "6047", "6053", "6803", "8053", "8059" ]
[ "nonn", "base", "fini", "full" ]
9
0
5
[ "A359136", "A359137", "A360040", "A360041" ]
null
Rémy Sigrist, Jan 23 2023
2023-01-23T09:10:00
oeisdata/seq/A360/A360041.seq
4448eb91dac6bc4752772af782eed380
A360042
Number of vertices in a Farey fan of order n.
[ "4", "6", "11", "17", "29", "39", "59", "79", "107", "133", "175", "213", "271", "323", "385", "451", "541", "621", "731", "835", "955", "1073", "1225", "1367", "1541", "1707", "1897", "2087", "2321", "2535", "2801", "3061", "3345", "3625", "3937", "4243", "4609", "4957", "5335", "5713", "6155", "6569", "7055", "7529", "8031", "8531", "9101", "9649", "10265", "10859" ]
[ "nonn" ]
18
0
5
[ "A005598", "A005728", "A174030", "A359690", "A359968", "A359974", "A360042", "A360043", "A360044" ]
null
Scott R. Shannon, N. J. A. Sloane and M. Douglas McIlroy Jan 23 2023
2023-01-30T10:34:33
oeisdata/seq/A360/A360042.seq
2c855f6d47219d35c135fca88131aa6f
A360043
Number of edges in a Farey fan of order n.
[ "4", "9", "18", "30", "52", "74", "112", "154", "210", "268", "352", "436", "552", "668", "802", "948", "1134", "1316", "1546", "1778", "2038", "2306", "2630", "2952", "3326", "3704", "4124", "4556", "5060", "5552", "6126", "6710", "7338", "7978", "8674", "9376", "10174", "10972", "11824", "12692", "13664", "14620", "15690", "16768", "17898", "19048", "20314", "21574", "22944", "24312" ]
[ "nonn" ]
8
0
5
[ "A005598", "A005728", "A174030", "A359693", "A359970", "A359976", "A360042", "A360043", "A360044" ]
null
Scott R. Shannon, N. J. A. Sloane and M. Douglas McIlroy, Jan 23 2023
2023-01-24T07:50:16
oeisdata/seq/A360/A360043.seq
dd35794896b138c589f115d8cbaf527c
A360044
Table read by rows: T(n,k) is the number of k-gons, 3<=k<=4, in a Farey fan of order n.
[ "0", "1", "4", "0", "6", "2", "10", "4", "14", "10", "22", "14", "30", "24", "42", "34", "54", "50", "74", "62", "94", "84", "118", "106", "142", "140", "178", "168", "214", "204", "258", "240", "302", "292", "358", "338", "414", "402", "478", "466", "542", "542", "626", "608", "710", "696", "802", "784", "894", "892", "1010", "988", "1126", "1102", "1254", "1216", "1382", "1358", "1526", "1492" ]
[ "nonn", "tabf" ]
16
0
5
[ "A005598", "A005728", "A174030", "A359694", "A359971", "A359977", "A360042", "A360043", "A360044" ]
null
Scott R. Shannon, N. J. A. Sloane and M. Douglas McIlroy , Jan 23 2023
2023-02-02T12:47:06
oeisdata/seq/A360/A360044.seq
4223cab8006cfb4aa561f98b6d68aed4
A360045
a(n) = Sum_{k=0..floor(n/3)} binomial(n+2,3*k+2) * Catalan(k).
[ "1", "3", "6", "11", "21", "42", "86", "180", "387", "852", "1908", "4329", "9933", "23013", "53748", "126386", "298953", "710847", "1698086", "4073181", "9806565", "23689555", "57401322", "139475190", "339767545", "829638396", "2030206248", "4978136133", "12229451631", "30095772966", "74184390468", "183139941384" ]
[ "nonn" ]
16
0
5
[ "A000108", "A086615", "A360045", "A360046", "A360047" ]
null
Seiichi Manyama, Jan 23 2023
2025-02-06T13:23:26
oeisdata/seq/A360/A360045.seq
c2d255c163246b4cd7f37e4d42e079fa
A360046
a(n) = Sum_{k=0..floor(n/4)} binomial(n+3,4*k+3) * Catalan(k).
[ "1", "4", "10", "20", "36", "64", "120", "240", "497", "1036", "2158", "4524", "9625", "20816", "45560", "100368", "221915", "492380", "1097302", "2457228", "5526666", "12474000", "28233600", "64061920", "145704327", "332174532", "758977386", "1737703780", "3985847284", "9157908736", "21074460512", "48569746368", "112096071675" ]
[ "nonn" ]
17
0
5
[ "A000108", "A086615", "A360045", "A360046", "A360047" ]
null
Seiichi Manyama, Jan 23 2023
2023-01-25T08:32:05
oeisdata/seq/A360/A360046.seq
4d3bc6282b76bf770855fb5be6ea8719
A360047
a(n) = Sum_{k=0..floor(n/5)} binomial(n+4,5*k+4) * Catalan(k).
[ "1", "5", "15", "35", "70", "127", "220", "385", "715", "1430", "3005", "6400", "13500", "28050", "57800", "119515", "250425", "533525", "1151975", "2504700", "5453176", "11856275", "25748450", "55962300", "121981725", "266968938", "586630515", "1292992795", "2855288480", "6311930460", "13963767356", "30919563310" ]
[ "nonn" ]
17
0
5
[ "A000108", "A086615", "A360045", "A360046", "A360047" ]
null
Seiichi Manyama, Jan 23 2023
2023-01-25T08:34:49
oeisdata/seq/A360/A360047.seq
f83308d1307531387b80260b0f1bdcc6
A360048
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+1,2*k+1) * Catalan(k).
[ "1", "2", "2", "0", "-3", "-2", "9", "24", "11", "-66", "-152", "-8", "587", "1082", "-438", "-5248", "-7733", "7942", "47502", "53792", "-105313", "-430118", "-343043", "1249800", "3866557", "1730018", "-13996096", "-34243896", "-1947203", "150962374", "296101865", "-121857184", "-1582561869", "-2468098042", "2529520766" ]
[ "sign" ]
12
0
5
[ "A000108", "A360048", "A360049", "A360050", "A360051" ]
null
Seiichi Manyama, Jan 23 2023
2023-01-25T08:36:30
oeisdata/seq/A360/A360048.seq
00cf2f66cbdc010eb403b60dd0e781ad
A360049
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n+2,3*k+2) * Catalan(k).
[ "1", "3", "6", "9", "9", "0", "-26", "-72", "-117", "-82", "204", "975", "2289", "3357", "1332", "-9834", "-37935", "-82593", "-108282", "2583", "487521", "1621071", "3261546", "3685230", "-2318615", "-24607854", "-72887472", "-134909701", "-123941901", "200330184", "1258932996", "3377359872", "5706502677", "3797618237" ]
[ "sign" ]
16
0
5
[ "A000108", "A360048", "A360049", "A360050", "A360051" ]
null
Seiichi Manyama, Jan 23 2023
2023-11-21T16:29:47
oeisdata/seq/A360/A360049.seq
2a196f572aa205e0da7052f0a0de7835
A360050
a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+3,4*k+3) * Catalan(k).
[ "1", "4", "10", "20", "34", "48", "48", "0", "-163", "-548", "-1274", "-2340", "-3255", "-2224", "5304", "28560", "82379", "182300", "322102", "410700", "133128", "-1295264", "-5440600", "-14733680", "-31384533", "-52870668", "-59633454", "11449780", "312532426", "1137823168", "2918752832", "5961965824", "9464314955" ]
[ "sign" ]
13
0
5
[ "A000108", "A360048", "A360049", "A360050", "A360051" ]
null
Seiichi Manyama, Jan 23 2023
2023-01-25T08:40:18
oeisdata/seq/A360/A360050.seq
9cc9eee723b1caf48654f1da33cc1621
A360051
a(n) = Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+4,5*k+4) * Catalan(k).
[ "1", "5", "15", "35", "70", "125", "200", "275", "275", "0", "-999", "-3610", "-9380", "-20570", "-39440", "-65251", "-85695", "-56435", "141735", "781770", "2413128", "5999325", "12921350", "24387900", "39098925", "46638744", "11740695", "-158571665", "-674961760", "-1956733020", "-4724183860", "-9957286550", "-18316004575" ]
[ "sign" ]
13
0
5
[ "A000108", "A360048", "A360049", "A360050", "A360051" ]
null
Seiichi Manyama, Jan 23 2023
2023-01-24T02:56:27
oeisdata/seq/A360/A360051.seq
2e012c10c4030421bd5ece64183c7ac1
A360052
Number of length n inversion sequences avoiding the patterns 010 and 201 (or 010 and 210).
[ "1", "1", "2", "5", "15", "53", "214", "958", "4650", "24103", "131974", "757011", "4519321", "27933252", "177987808", "1165057411", "7811122974", "53506838952", "373693431140", "2656088059747", "19182588092365", "140577110057850", "1044102585724522", "7851149068600037", "59714190403840142", "459001044591439621" ]
[ "nonn" ]
13
0
5
[ "A263777", "A263779", "A360052" ]
null
Benjamin Testart, Jan 23 2023
2024-07-12T09:51:47
oeisdata/seq/A360/A360052.seq
f0d3855ef84f2c5ae56dcc5d00907f7b
A360053
Primes p such that each prime < p in the prime factorization of 2^(p-1) - 1 has exponent 1.
[ "2", "3", "5", "11", "17", "23", "29", "47", "53", "59", "71", "83", "89", "107", "113", "131", "149", "167", "173", "179", "191", "197", "227", "233", "239", "251", "257", "263", "269", "293", "317", "347", "353", "359", "383", "389", "419", "431", "443", "449", "467", "479", "491", "503", "509", "557", "563", "569", "587", "593", "599", "617", "647", "653", "659", "677", "683" ]
[ "nonn" ]
34
0
5
null
null
Alain Rocchelli, Jan 23 2023
2023-02-08T13:14:55
oeisdata/seq/A360/A360053.seq
f81b3231cc14e6ea47b70b28676af8c7
A360054
Number of odd amicable pairs where the smaller term of the pair is less than 10^n.
[ "0", "0", "0", "0", "3", "8", "21", "55", "154", "412", "1088", "2632", "6532", "15371", "35218", "79982", "180061", "402560", "894404", "1975742" ]
[ "nonn", "more" ]
35
0
5
[ "A005408", "A066873", "A259180", "A262622", "A262623", "A262625", "A360054" ]
null
Zoltan Galantai, Jan 23 2023
2023-01-28T12:23:15
oeisdata/seq/A360/A360054.seq
55a8da129a2117fd48cee8366bf5d132
A360055
Number of L-connected free polyominoes with n cells (see comments for definition).
[ "1", "1", "1", "2", "4", "7", "14", "24", "48", "83", "155", "265", "472", "793", "1356", "2235", "3700", "5977", "9636", "15262", "24068", "37439", "57920", "88628", "134838", "203264", "304688", "453126", "670238", "984556", "1438878", "2089996", "3021162", "4343229", "6215668", "8851151", "12550775", "17716075", "24907961", "34873541", "48644474" ]
[ "nonn" ]
38
0
5
[ "A000105", "A126764", "A360055" ]
null
Allan C. Wechsler and John Mason, Jan 23 2023
2023-01-28T22:07:24
oeisdata/seq/A360/A360055.seq
29ff1a34640b454a6455d0a2edfbf0b0
A360056
a(n) is the position, counted from the right, of the rightmost nonzero value in the n-th nonzero restricted growth string in A239903 and its infinite continuation.
[ "1", "2", "1", "1", "3", "1", "2", "1", "1", "2", "1", "1", "1", "4", "1", "2", "1", "1", "3", "1", "2", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "5", "1", "2", "1", "1", "3", "1", "2", "1", "1", "2", "1", "1", "1", "4", "1", "2", "1", "1", "3", "1", "2", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "4", "1", "2", "1", "1", "3", "1" ]
[ "nonn" ]
37
0
5
[ "A239903", "A360056" ]
null
Italo J Dejter, Jan 23 2023
2024-08-05T05:34:58
oeisdata/seq/A360/A360056.seq
95e60b896e9ca258ab0dbb1f8d3c8d18
A360057
a(n) = Sum_{k=0..n} binomial(n+4*k+4,n-k) * Catalan(k).
[ "1", "6", "27", "125", "644", "3643", "21974", "138395", "898695", "5970927", "40386209", "277127148", "1924349756", "13496536510", "95467320600", "680260392219", "4878382821267", "35182209381590", "255000022472565", "1856501085686340", "13570366067586294", "99554601986349471", "732756800760507312" ]
[ "nonn" ]
28
0
5
[ "A000108", "A086616", "A162481", "A358518", "A360047", "A360057" ]
null
Seiichi Manyama, Jan 23 2023
2023-03-11T08:09:11
oeisdata/seq/A360/A360057.seq
5396bb4ce45156653207aa07b626c4c1
A360058
a(n) = Sum_{k=0..n} (-1)^k * binomial(n+2*k+2,n-k) * Catalan(k).
[ "1", "2", "2", "2", "3", "3", "2", "4", "5", "0", "4", "13", "-7", "-7", "48", "-16", "-93", "180", "74", "-584", "517", "1111", "-2850", "207", "8281", "-10738", "-11740", "46967", "-22167", "-115845", "211052", "94468", "-766989", "660110", "1554938", "-3983408", "121429", "12272689", "-15692006", "-18841086", "72792247", "-31828764" ]
[ "sign" ]
27
0
5
[ "A000108", "A162481", "A360049", "A360058", "A360059", "A360060" ]
null
Seiichi Manyama, Jan 23 2023
2023-03-11T08:42:31
oeisdata/seq/A360/A360058.seq
6297828710a9181e347141768478b98b
A360059
a(n) = Sum_{k=0..n} (-1)^k * binomial(n+3*k+3,n-k) * Catalan(k).
[ "1", "3", "4", "3", "5", "12", "6", "-13", "29", "95", "-130", "-304", "895", "1050", "-5068", "-2181", "27743", "-5481", "-143532", "117983", "700831", "-1074414", "-3163138", "7872784", "12585117", "-51587107", "-38040886", "312988334", "18178883", "-1779688404", "1013771196", "9485832411", "-11749675733", "-46878057651" ]
[ "sign" ]
25
0
5
[ "A000108", "A358518", "A360050", "A360058", "A360059", "A360060" ]
null
Seiichi Manyama, Jan 23 2023
2024-05-06T22:48:19
oeisdata/seq/A360/A360059.seq
31220cead4ecac40b8ba8c41e31c2626
A360060
a(n) = Sum_{k=0..n} (-1)^k * binomial(n+4*k+4,n-k) * Catalan(k).
[ "1", "4", "7", "5", "4", "29", "50", "-83", "-185", "743", "1425", "-5250", "-9868", "40530", "73280", "-319155", "-557485", "2573032", "4341065", "-21107670", "-34398290", "175655925", "276438452", "-1479202280", "-2247154681", "12581036223", "18440253397", "-107916225837", "-152514334540", "932452267956", "1269723550920" ]
[ "sign" ]
22
0
5
[ "A000108", "A360051", "A360057", "A360058", "A360059", "A360060" ]
null
Seiichi Manyama, Jan 23 2023
2023-01-25T08:13:30
oeisdata/seq/A360/A360060.seq
64622d746e739e4210a218d4b30a3a8b
A360061
Lexicographically earliest increasing sequence such that a(1) = 2 and for n >= 2, a(1)^2 + a(2)^2 + ... + a(n)^2 is a prime.
[ "2", "3", "4", "12", "48", "54", "66", "138", "144", "162", "168", "180", "198", "234", "252", "264", "330", "360", "366", "372", "402", "420", "444", "462", "480", "534", "546", "552", "564", "576", "600", "630", "642", "678", "702", "744", "756", "846", "852", "858", "882", "966", "1008", "1206", "1242", "1254", "1266", "1272", "1296", "1302", "1338", "1650" ]
[ "easy", "nonn" ]
37
0
5
[ "A051935", "A137326", "A360061" ]
null
Win Wang, Jan 23 2023
2025-02-03T09:37:03
oeisdata/seq/A360/A360061.seq
315ca4947442aa42e08b1ce1f03d6852
A360062
Triangle read by rows: T(m,n) is the number of spanning trees in the graph whose nodes are the integer lattice points (x,y) with 0 <= x < m and 0 <= y < n, and with an edge between two nodes if there is no other integer lattice point on the line segment between them; 1 <= n <= m.
[ "1", "1", "16", "1", "576", "496125", "1", "41616", "1830420480", "375297659043840", "1", "5085025", "10361547386325", "166557643451782840320", "5885897714143664700439342125", "1", "945193536", "144188666818560000", "258848560805325726352932864", "1192037309255692352595217996892160000", "36939045170346949681155330481716034613142893328" ]
[ "nonn", "tabl" ]
9
0
5
[ "A116469", "A247943", "A360062", "A360063" ]
null
Pontus von Brömssen, Jan 24 2023
2023-01-28T15:46:45
oeisdata/seq/A360/A360062.seq
1409d0b12c86b0a878261b006798d174
A360063
Triangle read by rows: T(m,n) is the number of Hamiltonian cycles in the graph whose nodes are the integer lattice points (x,y) with 0 <= x < m and 0 <= y < n, and with an edge between two nodes if there is no other integer lattice point on the line segment between them; 1 <= n <= m.
[ "0", "0", "3", "0", "24", "1152", "0", "354", "436416", "2595450592", "0", "8138", "129422880" ]
[ "nonn", "tabl", "more" ]
14
0
5
[ "A247943", "A247944", "A321172", "A360062", "A360063" ]
null
Pontus von Brömssen, Jan 24 2023
2023-02-18T08:07:35
oeisdata/seq/A360/A360063.seq
115aff8b542bb83d9472dc51816dcda6
A360064
Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes and trominos (L-shaped connection of 3 cubes).
[ "1", "5", "89", "1177", "16873", "237977", "3366793", "47599097", "673035625", "9516252633", "134553882441", "1902506043833", "26900227288361", "380352114739609", "5377937177440009", "76040613721296249", "1075165950495479017", "15202163218500810073", "214948926180739194569" ]
[ "nonn", "easy" ]
18
0
5
[ "A001045", "A006253", "A033516", "A335559", "A359885", "A359886", "A360064", "A360065", "A360066" ]
null
Gerhard Kirchner, Jan 30 2023
2024-10-02T07:30:40
oeisdata/seq/A360/A360064.seq
940e397d6dc6cafa694ae9ba596ffce8
A360065
Number of 3-dimensional tilings of a 2 X 2 X n box using 2 X 1 X 1 dominos and trominos (L-shaped connection of 3 cubes).
[ "1", "2", "45", "412", "4705", "50374", "549109", "5955544", "64683649", "702259786", "7625147293", "82791470836", "898931464993", "9760376329678", "105975828745957", "1150659965697328", "12493588746237697", "135652375422278290", "1472880803124594061", "15992184812239930060", "173639288800074705121" ]
[ "nonn", "easy" ]
16
0
5
[ "A001045", "A006253", "A033516", "A335559", "A359884", "A359885", "A360064", "A360065", "A360066" ]
null
Gerhard Kirchner, Jan 30 2023
2024-10-02T10:52:56
oeisdata/seq/A360/A360065.seq
a19de5b69a176532172b4e3435206f7e
A360066
Number of 3-dimensional tilings of a 2 X 2 X n box using 1 X 1 X 1 cubes, 2 X 1 X 1 dominos and trominos (L-shaped connection of 3 cubes).
[ "1", "11", "444", "13311", "422617", "13265660", "417336617", "13123557903", "412719195520", "12979269602143", "408175860119021", "12836425011761592", "403683424226081169", "12695147020245034099", "399240466722076292612", "12555423726269799691295", "394846409914451855949249" ]
[ "nonn" ]
16
0
5
[ "A001045", "A006253", "A033516", "A335559", "A359884", "A359885", "A360064", "A360065", "A360066" ]
null
Gerhard Kirchner, Jan 30 2023
2024-03-03T17:17:41
oeisdata/seq/A360/A360066.seq
7efbf9a5957efa946f251d1e9f6825e0
A360067
a(n) = det(M) where M is an n X n matrix with M[i,j] = i^j*(i-j).
[ "1", "0", "2", "12", "2304", "898560", "4827340800", "143219736576000", "49230909076930560000", "149334225705682285363200000", "5482643392499167214520238080000000", "2322479608280149573505226859610112000000000", "13283541711093841017468807905468592685056000000000000" ]
[ "nonn" ]
23
0
5
[ "A000178", "A060238", "A089064", "A152653", "A174890", "A176001", "A176005", "A360067" ]
null
José María Grau Ribas, Jan 24 2023
2024-04-19T07:11:55
oeisdata/seq/A360/A360067.seq
00be38947a8ef64259140bf0b7113bd7
A360068
Number of integer partitions of n such that the parts have the same mean as the multiplicities.
[ "1", "1", "0", "0", "1", "0", "0", "0", "2", "1", "0", "0", "6", "0", "0", "0", "6", "0", "7", "0", "1", "0", "0", "0", "0", "90", "0", "63", "0", "0", "0", "0", "11", "0", "0", "0", "436", "0", "0", "0", "0", "0", "0", "0", "0", "2157", "0", "0", "240", "1595", "22", "0", "0", "0", "6464", "0", "0", "0", "0", "0", "0", "0", "0", "11628", "4361", "0", "0", "0", "0", "0", "0", "0", "12927", "0", "0", "621", "0" ]
[ "nonn" ]
15
0
5
[ "A000009", "A000041", "A008284", "A058398", "A067340", "A067538", "A082550", "A088529", "A088530", "A112798", "A124010", "A240219", "A316313", "A326567", "A326568", "A327475", "A327482", "A349156", "A359893", "A359897", "A359903", "A359904", "A359905", "A360068", "A360069", "A360070" ]
null
Gus Wiseman, Jan 27 2023
2024-07-09T20:44:10
oeisdata/seq/A360/A360068.seq
224b4fbdc5a77dce960540754e1cba1f
A360069
Number of integer partitions of n whose multiset of multiplicities has integer mean.
[ "0", "1", "2", "3", "4", "5", "9", "9", "13", "16", "25", "26", "39", "42", "62", "67", "95", "107", "147", "168", "225", "245", "327", "381", "471", "565", "703", "823", "1038", "1208", "1443", "1743", "2088", "2439", "2937", "3476", "4163", "4921", "5799", "6825", "8109", "9527", "11143", "13122", "15402", "17887", "20995", "24506", "28546", "33234", "38661" ]
[ "nonn" ]
8
0
5
[ "A000009", "A000041", "A000975", "A008284", "A051293", "A058398", "A067340", "A067538", "A082550", "A088529", "A088530", "A102627", "A124010", "A240219", "A316313", "A316413", "A325347", "A326622", "A326669", "A327475", "A327482", "A328966", "A349156", "A359905", "A360068", "A360069" ]
null
Gus Wiseman, Jan 27 2023
2023-01-29T10:45:06
oeisdata/seq/A360/A360069.seq
ae683a31fce48283f42fe1f20cf52291
A360070
Numbers for which there exists an integer partition such that the parts have the same mean as the multiplicities.
[ "1", "4", "8", "9", "12", "16", "18", "20", "25", "27", "32", "36", "45", "48", "49", "50", "54", "63", "64", "72", "75", "80", "81", "90", "96", "98", "99", "100", "108", "112", "117", "121", "125", "128", "144", "147", "150", "160", "162", "169", "175", "176", "180", "192", "196", "200", "208", "216", "224", "225", "240", "242", "243", "245", "250", "252", "256", "272" ]
[ "nonn" ]
18
0
5
[ "A000009", "A000041", "A005117", "A008284", "A058398", "A067340", "A067538", "A088529", "A088530", "A112798", "A124010", "A240219", "A316313", "A326567", "A326568", "A327482", "A349156", "A359903", "A359904", "A359905", "A360068", "A360069", "A360070" ]
null
Gus Wiseman, Jan 27 2023
2023-01-29T21:02:11
oeisdata/seq/A360/A360070.seq
bb26dc372a42d127c1117228ffda0a2a
A360071
Regular tetrangle where T(n,k,i) = number of integer partitions of n of length k with i distinct parts.
[ "1", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "2", "0", "2", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "2", "1", "1", "1", "0", "2", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "3", "0", "3", "1", "0", "2", "1", "0", "0", "2", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "tabf" ]
9
0
5
[ "A000009", "A000041", "A008284", "A051731", "A055884", "A058398", "A060016", "A116608", "A318393", "A318816", "A320808", "A327482", "A331195", "A334433", "A345197", "A360010", "A360069", "A360071", "A360072" ]
null
Gus Wiseman, Jan 28 2023
2023-01-30T09:15:27
oeisdata/seq/A360/A360071.seq
097d699368c04c99a80e64ed27033309
A360072
Number of pairs of positive integers (k,i) such that k >= i and there exists an integer partition of n of length k with i distinct parts.
[ "0", "1", "2", "3", "5", "5", "9", "9", "13", "14", "18", "19", "26", "25", "30", "34", "39", "40", "48", "48", "56", "59", "64", "67", "78", "78", "84", "89", "97", "99", "111", "111", "121", "125", "131", "137", "149", "149", "158", "165", "176", "177", "190", "191", "202", "210", "216", "222", "238", "239", "250", "256", "266", "270", "284", "289", "302", "307", "316", "323" ]
[ "nonn" ]
12
0
5
[ "A000005", "A000009", "A000041", "A008284", "A051731", "A055884", "A058398", "A060016", "A116608", "A331195", "A360010", "A360071", "A360072" ]
null
Gus Wiseman, Jan 28 2023
2023-01-31T14:19:03
oeisdata/seq/A360/A360072.seq
6671af68504d87dc2ca746dafb1fb2ba
A360073
a(n) is the greatest divisor of n divisible by the product of its own digits.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "5", "11", "12", "1", "7", "15", "8", "1", "9", "1", "5", "7", "11", "1", "24", "5", "2", "9", "7", "1", "15", "1", "8", "11", "2", "7", "36", "1", "2", "3", "8", "1", "7", "1", "11", "15", "2", "1", "24", "7", "5", "3", "4", "1", "9", "11", "8", "3", "2", "1", "15", "1", "2", "9", "8", "5", "11", "1", "4", "3", "7", "1", "36", "1", "2", "15", "4", "11", "6", "1", "8", "9" ]
[ "nonn", "base", "easy" ]
11
0
5
[ "A007602", "A335037", "A337941", "A360073", "A360074" ]
null
Rémy Sigrist, Jan 24 2023
2023-01-27T03:13:55
oeisdata/seq/A360/A360073.seq
837d91055ddb5e222ff92a259c0ba519
A360074
a(n) is the greatest divisor of n divisible by the sum of its own digits.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "1", "12", "1", "7", "5", "8", "1", "18", "1", "20", "21", "2", "1", "24", "5", "2", "27", "7", "1", "30", "1", "8", "3", "2", "7", "36", "1", "2", "3", "40", "1", "42", "1", "4", "45", "2", "1", "48", "7", "50", "3", "4", "1", "54", "5", "8", "3", "2", "1", "60", "1", "2", "63", "8", "5", "6", "1", "4", "3", "70", "1", "72", "1", "2", "5", "4", "7", "6", "1", "80" ]
[ "nonn", "base", "easy" ]
12
0
5
[ "A005349", "A332268", "A360073", "A360074" ]
null
Rémy Sigrist, Jan 24 2023
2023-09-04T11:19:30
oeisdata/seq/A360/A360074.seq
b043a12070395ea761ee24490c7c81b0
A360075
a(n) is the product of the digits of A007602(n), the n-th Zuckerman number.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "1", "2", "5", "8", "18", "1", "2", "5", "16", "6", "15", "16", "35", "4", "12", "16", "6", "15", "96", "24", "12", "48", "84", "105", "48", "1", "2", "3", "5", "6", "3", "42", "32", "63", "4", "108", "3", "18", "48", "24", "175", "35", "4", "32", "24", "108", "3", "18", "144", "21", "252", "18", "135", "8", "64", "96", "96", "288", "108", "14", "63" ]
[ "nonn", "base" ]
9
0
5
[ "A007602", "A007954", "A051801", "A288069", "A325454", "A360075" ]
null
Rémy Sigrist, Jan 24 2023
2023-01-27T03:12:48
oeisdata/seq/A360/A360075.seq
a32df56b159e2b5ec0a4b65c2c1a6246
A360076
a(n) = Sum_{k=0..n} binomial(3*k,n-k) * Catalan(k).
[ "1", "1", "5", "20", "90", "430", "2136", "10937", "57307", "305822", "1656482", "9083432", "50328114", "281324294", "1584578746", "8984740485", "51242962251", "293772468164", "1691974930584", "9785378133297", "56805049768157", "330880419984832", "1933299689139364", "11328101469158554" ]
[ "nonn" ]
28
0
5
[ "A000108", "A052709", "A073155", "A099234", "A360076", "A360082", "A360083" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:08:17
oeisdata/seq/A360/A360076.seq
d4ad15ce00408b7304a1771af4948836
A360077
Odd numbers k such that k mod (k-s) = 1, where s is the greatest square < k.
[ "3", "7", "11", "13", "19", "21", "27", "29", "31", "33", "41", "43", "51", "53", "55", "57", "61", "67", "71", "73", "83", "85", "89", "91", "97", "103", "109", "111", "123", "125", "127", "129", "131", "133", "141", "155", "157", "171", "173", "175", "177", "181", "183", "193", "199", "201", "209", "211", "227", "229", "233", "239", "241", "253", "259", "261", "271", "273", "291" ]
[ "nonn" ]
17
0
5
[ "A002496", "A002522", "A360077" ]
null
Bill McEachen, Jan 24 2023
2023-02-13T04:33:49
oeisdata/seq/A360/A360077.seq
218f1057c60d14cd46a236c3fbb8a3f4
A360078
Moebius function for the floor quotient poset.
[ "1", "-1", "-1", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "0", "1", "1", "-1", "-1", "-1", "-1", "-1", "-1", "0", "0", "0", "-1", "-1", "-1", "-2", "-2", "-2", "-2", "-2", "-2", "-1", "-1", "-1", "-1", "0", "0", "-1", "-1", "-1", "-2", "-2", "-2", "-2", "-3", "-3", "-3", "-3", "-3", "-1", "-1", "-1", "-1", "-1", "-1", "1", "1", "1", "0", "-1", "-1", "-1", "-1", "-1", "-1", "-1" ]
[ "sign", "look" ]
26
0
5
[ "A002321", "A008683", "A360078", "A360079" ]
null
Harry Richman, Jan 24 2023
2024-02-14T20:17:56
oeisdata/seq/A360/A360078.seq
bc48d52deb21fe1ff833ceb62b90aa71
A360079
Finite differences of Moebius function for the floor quotient poset.
[ "1", "-2", "0", "1", "0", "1", "0", "-1", "1", "0", "0", "-1", "0", "0", "0", "1", "0", "-2", "0", "0", "0", "0", "0", "1", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "-1", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "2", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-2" ]
[ "sign" ]
16
0
5
[ "A002321", "A008683", "A360078", "A360079" ]
null
Harry Richman, Jan 24 2023
2024-01-01T19:49:38
oeisdata/seq/A360/A360079.seq
e8a03c53b6ff3f40434a0c4ba10041c1
A360080
Smallest k such that 2^(2^n) + k is a safe prime.
[ "1", "7", "7", "7", "91", "3103", "12451", "230191", "286867", "1657867", "10029811", "29761351", "22410151", "98402791", "167137543" ]
[ "nonn", "more", "hard" ]
22
0
5
[ "A005385", "A013597", "A013603", "A058220", "A181356", "A335313", "A350696", "A360080", "A360081" ]
null
Mark Andreas, Jan 25 2023
2023-01-29T17:52:24
oeisdata/seq/A360/A360080.seq
58894e9a0b040e7d94dc6ca05c02e324
A360081
Smallest k such that 2^(3*2^n) + k is a safe prime.
[ "3", "19", "31", "691", "907", "2887", "15943", "69283", "216127", "1108831", "8344423", "10976347", "166965391", "385465771", "26580643" ]
[ "nonn", "more", "hard" ]
21
0
5
[ "A005385", "A013597", "A013603", "A057821", "A181356", "A335313", "A350696", "A360080", "A360081" ]
null
Mark Andreas, Jan 25 2023
2023-01-27T15:26:59
oeisdata/seq/A360/A360081.seq
926167f30ad0f2000179f457f2037b7e
A360082
a(n) = Sum_{k=0..n} binomial(4*k,n-k) * Catalan(k).
[ "1", "1", "6", "27", "134", "709", "3892", "22004", "127250", "749230", "4476386", "27071344", "165398868", "1019405720", "6330482488", "39571612357", "248796862550", "1572300095758", "9981970108384", "63633339713190", "407162295120570", "2614059813642256", "16834457481559076" ]
[ "nonn" ]
8
0
5
[ "A000108", "A052709", "A073155", "A099235", "A360076", "A360082", "A360083" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:08:13
oeisdata/seq/A360/A360082.seq
c0cab365a988424e9cb2f04476147f67
A360083
a(n) = Sum_{k=0..n} binomial(5*k,n-k) * Catalan(k).
[ "1", "1", "7", "35", "189", "1092", "6538", "40278", "253730", "1626858", "10582616", "69669273", "463319257", "3107941405", "21004392887", "142882885210", "977562617826", "6722361860888", "46438235933700", "322111000796428", "2242538435656450", "15665017062799230", "109761527468995102" ]
[ "nonn" ]
7
0
5
[ "A000108", "A052709", "A073155", "A360076", "A360082", "A360083", "A360090" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:08:08
oeisdata/seq/A360/A360083.seq
9489fd481ed1b0cc8980f3014ce9401d
A360084
a(n) = Sum_{k=0..n} (-1)^k * binomial(3*k,n-k) * Catalan(k).
[ "1", "-1", "-1", "4", "-2", "-14", "36", "-1", "-191", "418", "182", "-2904", "5546", "5226", "-47466", "78843", "121489", "-813060", "1157400", "2659695", "-14364997", "17078752", "56866292", "-259091498", "246553176", "1202210486", "-4736784794", "3346401868", "25255328948", "-87323306720", "39123129700" ]
[ "sign" ]
8
0
5
[ "A000108", "A360084", "A360085", "A360086" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:08:04
oeisdata/seq/A360/A360084.seq
6bc6e134bb142009f123ae602af04552
A360085
a(n) = Sum_{k=0..n} (-1)^k * binomial(4*k,n-k) * Catalan(k).
[ "1", "-1", "-2", "5", "6", "-37", "12", "236", "-454", "-1038", "5258", "-688", "-41780", "79528", "212032", "-1067717", "99414", "9232114", "-17976592", "-49506598", "255604634", "-28864080", "-2294742268", "4618754686", "12550067560", "-67132100862", "10660021188", "612813797856", "-1280237246540", "-3357371054108" ]
[ "sign" ]
7
0
5
[ "A000108", "A360084", "A360085", "A360086" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:07:59
oeisdata/seq/A360/A360085.seq
7fb8badb03f0bf550a846295217b97b1
A360086
a(n) = Sum_{k=0..n} (-1)^k * binomial(5*k,n-k) * Catalan(k).
[ "1", "-1", "-3", "5", "19", "-52", "-114", "570", "470", "-6026", "2156", "59311", "-93869", "-519805", "1668241", "3635670", "-23289426", "-11134840", "280455900", "-238282316", "-2944763030", "6683843250", "25804836482", "-113673966635", "-155130413515", "1570407337023", "-253144380823", "-18639853806224" ]
[ "sign" ]
7
0
5
[ "A000108", "A360084", "A360085", "A360086" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:07:55
oeisdata/seq/A360/A360086.seq
3680505f5a8d812178ed158be6dae176
A360087
a(n) = Sum_{k=0..n} (-1)^k * binomial(3*k,n-k).
[ "1", "-1", "-2", "2", "6", "-5", "-17", "12", "48", "-28", "-135", "63", "378", "-134", "-1054", "259", "2927", "-408", "-8096", "280", "22305", "1551", "-61210", "-10638", "167310", "46683", "-455489", "-175852", "1234960", "612380", "-3334215", "-2031953", "8962498", "6523626", "-23981046", "-20445373", "63855135", "62900496" ]
[ "sign", "easy" ]
12
0
5
[ "A077979", "A099234", "A360087", "A360088", "A360089" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:07:38
oeisdata/seq/A360/A360087.seq
a10fa45cdfea26fdbe0c4da2d5a65d49
A360088
a(n) = Sum_{k=0..n} (-1)^k * binomial(4*k,n-k).
[ "1", "-1", "-3", "1", "13", "4", "-49", "-46", "165", "284", "-476", "-1417", "1003", "6220", "-110", "-24644", "-14831", "88184", "113224", "-278288", "-619744", "715647", "2891977", "-1036173", "-12068353", "-3381661", "45588556", "41600921", "-154355594", "-259984429", "448828716", "1305250324", "-964837159", "-5754843123" ]
[ "sign", "easy" ]
11
0
5
[ "A077979", "A099235", "A360087", "A360088", "A360089" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:07:42
oeisdata/seq/A360/A360088.seq
a9363ae1b6767da26146ecbc30bee1a9
A360089
a(n) = Sum_{k=0..n} (-1)^k * binomial(5*k,n-k).
[ "1", "-1", "-4", "-1", "21", "29", "-80", "-244", "153", "1473", "836", "-6920", "-12220", "23209", "91213", "-21511", "-510680", "-457965", "2210520", "4921941", "-6271749", "-33288595", "-3876765", "173223185", "214943855", "-682969376", "-1912499375", "1498348275", "11882164650", "5332839025", "-57402248250", "-92821609874" ]
[ "sign", "easy" ]
13
0
5
[ "A077979", "A360087", "A360088", "A360089", "A360090" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:07:46
oeisdata/seq/A360/A360089.seq
56a40414cce364e22e750457e93ff855
A360090
a(n) = Sum_{k=0..n} binomial(5*k,n-k).
[ "1", "1", "6", "21", "71", "251", "882", "3088", "10829", "37975", "133146", "466852", "1636944", "5739647", "20125051", "70564951", "247423522", "867546829", "3041899638", "10665883415", "37398034921", "131129599227", "459782762029", "1612146986543", "5652708454881", "19820223058176", "69496108849357" ]
[ "nonn", "easy" ]
13
0
5
[ "A002478", "A099234", "A099235", "A360090" ]
null
Seiichi Manyama, Jan 25 2023
2023-01-25T09:07:51
oeisdata/seq/A360/A360090.seq
4a1d3b19e21e2cc8734b130df3355214
A360091
Numerator of (n-2)!*Sum_{k=1..n} (-1)^(k+1)/((n-k)!*k^k).
[ "3", "31", "517", "322537", "2840123", "324200318207", "1285595921612117", "73566451396634047493", "44670351166870486810889", "1129160781485410557635298647751929", "1103929347366548607910442339939699", "25219262227183500148649140605496240723288052699" ]
[ "nonn", "frac" ]
26
0
5
[ "A001620", "A360091", "A360092" ]
null
Michel Marcus, Jan 25 2023
2023-12-09T17:15:51
oeisdata/seq/A360/A360091.seq
c4ddeb8332f7a1a57b255b4f344ccec0
A360092
Denominator of (n-2)!*Sum_{k=1..n} (-1)^(k+1)/((n-k)!*k^k).
[ "4", "108", "3456", "3600000", "48600000", "8004837960000", "43717088378880000", "3319007595022909440000", "2592974683611648000000000", "82200659870363161557652992000000000", "98640791844435793869183590400000000", "2715985485838884679142342027478742851379200000000" ]
[ "nonn", "frac" ]
18
0
5
[ "A360091", "A360092" ]
null
Michel Marcus, Jan 25 2023
2023-01-26T03:39:36
oeisdata/seq/A360/A360092.seq
a03ed7b92b60c99252a3b758a32283b7
A360093
a(n) is the smallest positive integer which can be represented as the sum of distinct partition numbers in exactly n ways, or -1 if no such integer exists.
[ "1", "3", "8", "15", "18", "23", "30", "33", "38", "43", "45", "48", "56", "58", "63", "71", "74", "-1", "78", "80", "85", "90", "93", "100", "101", "106", "104", "109", "113", "115", "119", "122", "130", "-1", "134", "135", "145", "141", "150", "153", "146", "149", "163", "156", "158", "165", "167", "173", "-1", "176", "178", "182", "181", "-1", "183", "186", "196", "193", "191", "199" ]
[ "sign" ]
5
0
5
[ "A000041", "A280253", "A360093" ]
null
Ilya Gutkovskiy, Jan 25 2023
2025-02-16T08:34:04
oeisdata/seq/A360/A360093.seq
fbe7a1eefaccb6e29fd708744b4c941c
A360094
Decimal expansion of Sum_{p primes, p == 1 mod 4} log(p)/p^2.
[ "1", "0", "7", "3", "5", "9", "5", "4", "5", "2", "9", "7", "1", "1", "3", "0", "7", "7", "1", "3", "8", "4", "5", "0", "3", "8", "2", "0", "0", "9", "1", "2", "1", "9", "0", "1", "1", "6", "6", "3", "3", "9", "3", "9", "6", "9", "1", "2", "6", "3", "7", "7", "7", "9", "3", "7", "2", "6", "5", "9", "5", "8", "0", "7", "8", "0", "2", "7", "8", "7", "7", "0", "5", "8", "5", "0", "7", "3", "6", "8", "7", "8", "6", "3", "9", "9", "6", "4", "6", "6", "5", "0", "7", "6", "5", "7", "2", "0", "1", "0", "1", "9", "5", "1", "4", "1" ]
[ "nonn", "cons" ]
9
0
5
[ "A085548", "A086032", "A086239", "A136271", "A358789", "A360094", "A360095" ]
null
Vaclav Kotesovec, Jan 25 2023
2023-01-25T10:01:19
oeisdata/seq/A360/A360094.seq
4fe2ff3367fb1c18f80bef5b34ab8587
A360095
Decimal expansion of Sum_{p primes, p == 3 (mod 4)} log(p)/p^2.
[ "2", "1", "2", "4", "4", "4", "7", "6", "8", "9", "3", "1", "6", "6", "5", "0", "5", "7", "7", "0", "5", "0", "6", "7", "7", "9", "2", "6", "8", "2", "8", "2", "5", "2", "1", "4", "8", "7", "0", "3", "7", "3", "6", "9", "5", "8", "4", "3", "7", "6", "6", "6", "9", "7", "8", "1", "0", "4", "9", "7", "5", "3", "7", "1", "6", "7", "7", "0", "9", "5", "9", "7", "6", "0", "2", "0", "8", "1", "1", "5", "3", "5", "8", "9", "6", "1", "3", "7", "0", "5", "9", "6", "1", "4", "0", "7", "4", "3", "8", "3", "3", "7", "4", "4", "7", "3" ]
[ "nonn", "cons" ]
11
0
5
[ "A085548", "A085991", "A086239", "A136271", "A358789", "A360094", "A360095" ]
null
Vaclav Kotesovec, Jan 25 2023
2023-03-02T21:25:23
oeisdata/seq/A360/A360095.seq
2bffc18675cb389ddeb968e232fc4b9c
A360096
To get a(n), replace 0's in the binary expansion of n with (-1) and interpret the result in base n.
[ "0", "1", "1", "4", "11", "21", "41", "57", "439", "640", "909", "1222", "1859", "2354", "2953", "3616", "61167", "78303", "98837", "123121", "152379", "185641", "224113", "268227", "344999", "405601", "473901", "550423", "637363", "732483", "837929", "954305", "32472031", "37912414", "44058661", "50977186", "58741163", "67420476" ]
[ "nonn", "base" ]
12
0
5
[ "A030300", "A057427", "A360096", "A360099" ]
null
Alois P. Heinz, Jan 25 2023
2023-01-30T18:38:41
oeisdata/seq/A360/A360096.seq
801ef93243563272bb6878ac95d1b97a
A360097
a(n) = smallest k such that 2*n*k-1 and 2*n*k+1 are nonprimes.
[ "13", "14", "20", "7", "5", "10", "4", "4", "8", "6", "7", "5", "1", "2", "4", "2", "1", "4", "2", "3", "17", "4", "2", "3", "1", "4", "4", "1", "2", "2", "2", "1", "8", "3", "8", "2", "4", "1", "8", "2", "3", "11", "1", "2", "10", "1", "1", "3", "4", "3", "2", "2", "4", "2", "2", "5", "3", "1", "1", "1", "1", "1", "9", "4", "2", "4", "1", "4", "3", "4", "1", "1", "1", "2", "2", "2", "1", "4", "3", "1", "2", "2", "4", "7", "1" ]
[ "nonn" ]
17
0
5
[ "A018252", "A124522", "A360097" ]
null
Tamas Sandor Nagy, Jan 25 2023
2023-02-09T09:39:13
oeisdata/seq/A360/A360097.seq
b0cb7728291b99273e8654cf12d9cc92
A360098
Square array read by antidiagonals upwards: T(n,k) is the number of ways of choosing nonnegative numbers for k n-sided dice, k >= 0, n >= 1, so that summing the faces can give any integer from 0 to n^k - 1.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "15", "1", "1", "1", "1", "1", "7", "1", "105", "1", "1", "1", "1", "1", "1", "71", "1", "945", "1", "1", "1", "1", "1", "10", "1", "1001", "1", "10395", "1", "1", "1", "1", "1", "3", "280", "1", "18089", "1", "135135", "1", "1", "1", "1", "1", "7", "15", "15400", "1", "398959", "1" ]
[ "nonn", "tabl" ]
24
0
5
[ "A001147", "A002119", "A025035", "A025036", "A060540", "A118914", "A131514", "A273013", "A360098" ]
null
William P. Orrick, Jan 25 2023
2023-02-18T15:28:51
oeisdata/seq/A360/A360098.seq
6101502bcde7e76e97deec47d3bacc9c
A360099
To get A(n,k), replace 0's in the binary expansion of n with (-1) and interpret the result in base k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "0", "0", "1", "0", "1", "-1", "0", "1", "0", "1", "0", "1", "1", "2", "-1", "0", "1", "2", "3", "-1", "1", "0", "1", "3", "4", "1", "1", "-1", "0", "1", "4", "5", "5", "3", "1", "1", "0", "1", "5", "6", "11", "7", "5", "3", "-1", "0", "1", "6", "7", "19", "13", "11", "7", "-2", "1", "0", "1", "7", "8", "29", "21", "19", "13", "1", "0", "-1", "0", "1", "8", "9", "41", "31", "29", "21", "14", "3", "0", "1", "0", "1", "9", "10", "55", "43", "41", "31", "43", "16", "5", "2", "-1" ]
[ "sign", "tabl", "look", "base" ]
25
0
5
[ "A000004", "A000012", "A000027", "A002061", "A006257", "A023443", "A030300", "A057427", "A062157", "A062158", "A083074", "A145037", "A147991", "A147992", "A147993", "A152618", "A153777", "A165900", "A359925", "A360096", "A360099" ]
null
Alois P. Heinz, Jan 25 2023
2023-02-03T11:32:40
oeisdata/seq/A360/A360099.seq
f2f091e7bac5c9ff60f3084f5cecaf4c
A360100
a(n) = Sum_{k=0..n} binomial(n+2*k-1,n-k) * Catalan(k).
[ "1", "1", "5", "23", "111", "562", "2952", "15948", "88076", "495077", "2823293", "16295020", "95007654", "558765743", "3310999269", "19748462718", "118471172054", "714355994997", "4327148812557", "26319195869861", "160677354596769", "984236344800234", "6047526697800992", "37262944840704171" ]
[ "nonn" ]
21
0
5
[ "A000108", "A002212", "A006319", "A162475", "A162481", "A258973", "A360100", "A360101", "A360102" ]
null
Seiichi Manyama, Jan 25 2023
2023-08-16T08:21:59
oeisdata/seq/A360/A360100.seq
ededab074bff4d06e0fbebb267d63a78