Datasets:
christopher
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oeis

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timestamp[us]date
1999-12-11 03:00:00
2025-04-25 01:21:50
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32
32
A002501
a(n) = 7^n - 3*4^n + 2*3^n.
[ "1", "19", "205", "1795", "14221", "106819", "778765", "5581315", "39606541", "279447619", "1965098125", "13792018435", "96690872461", "677427332419", "4744368982285", "33220131761155", "232579232659981", "1628208214321219", "11398072876175245", "79788974736297475", "558532690864457101" ]
[ "nonn", "easy" ]
48
0
5
[ "A001047", "A002501", "A002502", "A005333", "A093732", "A093733", "A262307" ]
[ "M5078", "N2197" ]
N. J. A. Sloane
2023-10-17T01:04:27
oeisdata/seq/A002/A002501.seq
edab15e64249a52f33bbe736b498c741
A002502
Number of connected relations.
[ "1", "65", "1795", "36317", "636331", "10365005", "162470155", "2495037197", "37898120011", "572284920845", "8614868501515", "129467758660877", "1943971108806091", "29175170378428685", "437752102106036875", "6567275797761209357" ]
[ "nonn", "nice", "easy" ]
32
0
5
[ "A001047", "A002501", "A002502", "A005333", "A093732", "A093733", "A262307" ]
[ "M5336", "N2323" ]
N. J. A. Sloane
2022-01-29T01:05:52
oeisdata/seq/A002/A002502.seq
dfb56826db116097b54499f5cde600ed
A002503
Numbers k such that binomial(2*k,k) is divisible by (k+1)^2.
[ "5", "14", "27", "41", "44", "65", "76", "90", "109", "125", "139", "152", "155", "169", "186", "189", "203", "208", "209", "219", "227", "230", "237", "265", "275", "298", "307", "311", "314", "321", "324", "329", "344", "377", "413", "419", "428", "434", "439", "441", "449", "458", "459", "467", "475" ]
[ "nonn", "easy", "nice" ]
42
0
5
[ "A000108", "A000396", "A002503", "A065344", "A065349", "A065350", "A067348", "A135627" ]
[ "M3840", "N1573" ]
N. J. A. Sloane, Mira Bernstein
2021-03-28T07:01:58
oeisdata/seq/A002/A002503.seq
b36220c7c111c3ff456f7a90e6c46493
A002504
Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407).
[ "2", "3", "4", "5", "7", "10", "11", "12", "14", "15", "18", "24", "25", "26", "28", "29", "31", "33", "35", "38", "39", "42", "43", "46", "49", "50", "53", "56", "59", "63", "64", "67", "68", "75", "81", "82", "87", "89", "91", "92", "94", "96", "106", "109", "120", "124", "126", "129", "130", "137", "141", "143", "148", "154", "157", "158", "159", "165", "166", "171", "172" ]
[ "nonn" ]
63
0
5
[ "A002407", "A002504", "A111251", "A121259" ]
[ "M0522", "N0188" ]
N. J. A. Sloane
2024-02-22T13:34:13
oeisdata/seq/A002/A002504.seq
0b183d701e0cdda6a9a8a6b0c1992c57
A002505
Nearest integer to the n-th Gram point.
[ "18", "23", "28", "32", "35", "39", "42", "46", "49", "52", "55", "58", "60", "63", "66", "68", "71", "74", "76", "79", "81", "84", "86", "88", "91", "93", "95", "98", "100", "102", "104", "107", "109", "111", "113", "115", "118", "120", "122", "124", "126" ]
[ "nonn" ]
73
0
5
[ "A002505", "A114857", "A114858", "A273061" ]
[ "M5052", "N2185" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002505.seq
e7dc0d38ab85454613fce126be9ae959
A002506
Denominators of coefficients of expansion of Bessel function J_2(x).
[ "8", "96", "3072", "184320", "17694720", "2477260800", "475634073600", "119859786547200", "38355131695104000", "15188632151261184000", "7290543432605368320000", "4170190843450270679040000", "2802368246798581896314880000" ]
[ "nonn" ]
17
0
5
[ "A002454", "A002474", "A002506", "A014401", "J0", "J1", "J3" ]
null
N. J. A. Sloane
2023-10-17T05:43:35
oeisdata/seq/A002/A002506.seq
e27bb5d5fb52d4c6dd630817e1cc93dc
A002507
Expansion of a modular function for Gamma_0(6).
[ "1", "2", "-5", "-24", "-23", "76", "249", "168", "-599", "-1670", "-1026", "3272", "8529", "5232", "-14062", "-35976", "-22337", "51516", "131617", "82568", "-169376", "-432636", "-273332", "513584", "1309800", "830372", "-1456569", "-3709672", "-2354215", "3904696", "9931407", "6301120", "-9983208", "-25339626", "-16057040", "24504584", "62033318" ]
[ "sign", "easy" ]
30
0
5
[ "A002507", "A002508", "A105559", "A128632", "A128633" ]
[ "M1542", "N0602" ]
N. J. A. Sloane
2021-12-20T20:25:56
oeisdata/seq/A002/A002507.seq
e6419c4ec4eacc37d96fe148b9044a5c
A002508
Expansion of a modular function for Gamma_0(6).
[ "1", "-2", "9", "-4", "28", "18", "118", "80", "504", "466", "1631", "2160", "5466", "7498", "17658", "25088", "51944", "78660", "149099", "226544", "412920", "627830", "1090006", "1671840", "2796805", "4263984", "6969690", "10555224", "16836620", "25396506", "39699240", "59409184", "91460952", "135795598", "205951071", "303740496", "454672142" ]
[ "sign", "easy" ]
26
0
5
[ "A002507", "A002508", "A002509" ]
[ "M1910", "N0754" ]
N. J. A. Sloane
2018-04-09T08:24:51
oeisdata/seq/A002/A002508.seq
a7a4eb753be9d88faeeeceb6f72fc8be
A002509
Expansion of a modular function for Gamma_0(14).
[ "1", "-1", "4", "-5", "15", "-19", "45", "-52", "118", "-137", "281", "-316", "625", "-695", "1331", "-1444", "2696", "-2907", "5308", "-5640", "10122", "-10650", "18845", "-19628", "34241", "-35378", "61036", "-62524", "106783", "-108593", "183799", "-185646", "311625", "-312800", "521232", "-520044", "860728", "-854151", "1404871", "-1386868", "2267960", "-2228161" ]
[ "sign", "easy" ]
25
0
5
null
[ "M3256", "N1314" ]
N. J. A. Sloane
2018-04-09T11:00:44
oeisdata/seq/A002/A002509.seq
0f19fbff0e65090a00d8947a5938ebe5
A002510
Expansion of a modular function for Gamma_0(15).
[ "1", "1", "2", "8", "10", "24", "53", "74", "153", "280", "436", "793", "1322", "2085", "3510", "5648", "8796", "14042", "21921", "33490", "51796", "78843", "118108", "178029", "265225", "390852", "576946", "843694", "1224329", "1775450", "2556360", "3658111", "5224159", "7418887", "10481780", "14773012", "20723154", "28941023" ]
[ "nonn", "easy" ]
32
0
5
null
[ "M1825", "N0725" ]
N. J. A. Sloane
2021-12-20T20:25:28
oeisdata/seq/A002/A002510.seq
dc287bdebd827147b4fe8aecf3ba0355
A002511
Expansion of a modular function for Gamma_0(21).
[ "1", "1", "2", "6", "8", "13", "29", "44", "66", "122", "184", "269", "448", "668", "972", "1505", "2205", "3153", "4677", "6717", "9480", "13656", "19245", "26793", "37714", "52301", "71894", "99392", "135969", "184637", "251492", "339793", "456432", "613837", "820388", "1091154", "1451243", "1920637", "2531468" ]
[ "nonn", "easy" ]
32
0
5
null
[ "M1566", "N0610" ]
N. J. A. Sloane
2018-04-09T08:05:47
oeisdata/seq/A002/A002511.seq
dd79d2c197d6ef11d3ce9d11eca5283f
A002512
Expansion of chi(x)^10 / phi(x)^4 in powers of x where phi(), chi() are Ramanujan theta functions.
[ "1", "2", "5", "10", "22", "40", "75", "130", "230", "382", "636", "1022", "1645", "2570", "4002", "6110", "9297", "13910", "20715", "30462", "44597", "64584", "93085", "132990", "189164", "266992", "375192", "523800", "728285", "1006684", "1386043", "1898586", "2591120", "3519840", "4764736", "6423032" ]
[ "nonn" ]
32
0
5
[ "A000122", "A000700", "A002512", "A010054", "A121373" ]
[ "M1380", "N0539" ]
N. J. A. Sloane, Simon Plouffe
2018-03-08T02:50:45
oeisdata/seq/A002/A002512.seq
4bf0b769fcd7ff79e314e3d732bdd05c
A002513
Number of "cubic partitions" of n: expansion of Product_{k>0} 1/((1-x^(2k))^2*(1-x^(2k-1))) in powers of x.
[ "1", "1", "3", "4", "9", "12", "23", "31", "54", "73", "118", "159", "246", "329", "489", "651", "940", "1242", "1751", "2298", "3177", "4142", "5630", "7293", "9776", "12584", "16659", "21320", "27922", "35532", "46092", "58342", "75039", "94503", "120615", "151173", "191611", "239060", "301086", "374026", "468342", "579408", "721638", "889287" ]
[ "nonn", "easy", "nice" ]
125
0
5
[ "A000122", "A001934", "A002513", "A015128", "A089799", "A215947", "A273225", "A319455" ]
[ "M2354", "N0930", "N0931" ]
N. J. A. Sloane, Simon Plouffe
2024-02-07T09:01:35
oeisdata/seq/A002/A002513.seq
52e5a03663c49f8f2b1a0089125c61e5
A002514
Coefficients in the asymptotic expansions of modified Hankel functions h_1(z) and h_2(z), rounded to nearest integer.
[ "0", "0", "0", "0", "1", "3", "15", "79", "474", "3207", "24087", "198923", "1791902", "17484377", "183707380", "2067904033", "24827519376", "316694549817", "4277112686513", "60971132411393", "914869422343564", "14413525170009350", "237888443951757586", "4104608160094692304" ]
[ "nonn" ]
25
0
5
null
[ "M2992", "N1212" ]
N. J. A. Sloane
2015-10-19T01:27:30
oeisdata/seq/A002/A002514.seq
b3e3a38e99be944285c8aa91971b6201
A002515
Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.
[ "3", "11", "23", "83", "131", "179", "191", "239", "251", "359", "419", "431", "443", "491", "659", "683", "719", "743", "911", "1019", "1031", "1103", "1223", "1439", "1451", "1499", "1511", "1559", "1583", "1811", "1931", "2003", "2039", "2063", "2339", "2351", "2399", "2459", "2543", "2699", "2819", "2903", "2939", "2963", "3023", "3299" ]
[ "nonn", "easy" ]
59
0
5
[ "A002145", "A002515", "A005384" ]
[ "M2884", "N2039" ]
N. J. A. Sloane
2025-04-03T14:59:50
oeisdata/seq/A002/A002515.seq
750c9ea84f98789f716a5aa4f94dfdbf
A002516
Earliest sequence with a(a(n)) = 2n.
[ "0", "3", "6", "2", "12", "7", "4", "10", "24", "11", "14", "18", "8", "15", "20", "26", "48", "19", "22", "34", "28", "23", "36", "42", "16", "27", "30", "50", "40", "31", "52", "58", "96", "35", "38", "66", "44", "39", "68", "74", "56", "43", "46", "82", "72", "47", "84", "90", "32", "51", "54", "98", "60", "55", "100", "106", "80", "59", "62", "114", "104", "63", "116", "122", "192", "67", "70", "130" ]
[ "nonn", "nice" ]
52
0
5
[ "A002516", "A002517", "A004767", "A007379", "A017089", "A091067" ]
null
Colin Mallows
2021-09-20T04:38:27
oeisdata/seq/A002/A002516.seq
ee5a4d748d7e0bded83409600d9ec1ae
A002517
Earliest sequence with a(a(n))=3n.
[ "0", "2", "3", "6", "5", "12", "9", "8", "21", "18", "11", "30", "15", "14", "39", "36", "17", "48", "27", "20", "57", "24", "23", "66", "63", "26", "75", "54", "29", "84", "33", "32", "93", "90", "35", "102", "45", "38", "111", "42", "41", "120", "117", "44", "129", "108", "47", "138", "51", "50", "147", "144", "53", "156", "81", "56", "165", "60", "59", "174", "171", "62", "183", "72", "65", "192" ]
[ "nonn", "nice", "easy" ]
17
0
5
[ "A002516", "A002517", "A005843", "A007379", "A007494", "A016789", "A017197" ]
null
Colin Mallows
2016-08-28T18:23:33
oeisdata/seq/A002/A002517.seq
c716ec50b890e890a1218c73ad589646
A002518
Earliest sequence with a(a(n))=5n.
[ "0", "2", "5", "4", "15", "10", "7", "30", "9", "40", "25", "12", "55", "14", "65", "20", "17", "80", "19", "90", "75", "22", "105", "24", "115", "50", "27", "130", "29", "140", "35", "32", "155", "34", "165", "150", "37", "180", "39", "190", "45", "42", "205", "44", "215", "200", "47", "230", "49", "240", "125", "52", "255", "54", "265", "60", "57", "280", "59", "290", "275", "62", "305" ]
[ "nonn", "nice" ]
15
0
5
[ "A002516", "A002517", "A002518", "A007379" ]
null
Colin Mallows
2016-08-28T18:23:33
oeisdata/seq/A002/A002518.seq
8359e9e4498d9816e1e492e08d333723
A002519
Theta series of 28-dimensional unimodular lattice with no roots and a parity vector of norm 4.
[ "1", "0", "0", "1728", "106472", "1734912", "19335168", "141575552", "805208040", "3725209088", "14647517184", "50579062848", "156715230240", "443680116992", "1162915024896", "2851005884544", "6596700471272", "14509559545344", "30507866603520" ]
[ "nonn" ]
24
0
5
[ "A002519", "A002520" ]
null
N. J. A. Sloane
2023-10-17T05:44:05
oeisdata/seq/A002/A002519.seq
4ce13d3bea8715a61a8696c8621ea26b
A002520
Theta series of 28-dimensional unimodular lattice with no roots and with no parity vector of norm 4.
[ "1", "0", "0", "2240", "98280", "1790208", "19138560", "141920640", "805208040", "3723722240", "14651449344", "50573436480", "156717687840", "443691198720", "1162883174400", "2851049534592", "6596666916840", "14509544394240", "30507984568320" ]
[ "nonn", "nice", "easy" ]
17
0
5
[ "A002519", "A002520" ]
null
N. J. A. Sloane
2022-01-29T01:04:45
oeisdata/seq/A002/A002520.seq
85ef50bd1b3af29306416d759d735e4b
A002521
Weight distribution of [ 28,14,9 ] ternary self-dual code.
[ "1", "0", "0", "2184", "78624", "768096", "2159976", "1555632", "216216", "2240" ]
[ "nonn", "fini", "full" ]
11
0
5
null
null
N. J. A. Sloane
2023-10-16T23:43:47
oeisdata/seq/A002/A002521.seq
35ed9611857db3fe03ed6ecab498df1d
A002522
a(n) = n^2 + 1.
[ "1", "2", "5", "10", "17", "26", "37", "50", "65", "82", "101", "122", "145", "170", "197", "226", "257", "290", "325", "362", "401", "442", "485", "530", "577", "626", "677", "730", "785", "842", "901", "962", "1025", "1090", "1157", "1226", "1297", "1370", "1445", "1522", "1601", "1682", "1765", "1850", "1937", "2026", "2117", "2210", "2305", "2402", "2501" ]
[ "nonn", "easy" ]
423
0
5
[ "A000027", "A000124", "A000125", "A000127", "A002496", "A002522", "A005408", "A005843", "A006261", "A016813", "A020725", "A027383", "A028872", "A031396", "A051890", "A055096", "A058331", "A059100", "A059592", "A061547", "A062318", "A080856", "A086514", "A087475", "A094626", "A101220", "A114949", "A117619", "A117950", "A117951", "A124808", "A132411", "A132414", "A161701", "A161704", "A161706", "A161707", "A161708", "A161710", "A161713", "A161715", "A188377", "A198300", "A198306", "A198307", "A198308", "A198309", "A198310", "A254858", "A302612", "A302644", "A302645", "A302646" ]
null
N. J. A. Sloane
2025-04-09T22:17:32
oeisdata/seq/A002/A002522.seq
b77ca4fb41064b189494e360f1ea0f22
A002523
a(n) = n^4 + 1.
[ "1", "2", "17", "82", "257", "626", "1297", "2402", "4097", "6562", "10001", "14642", "20737", "28562", "38417", "50626", "65537", "83522", "104977", "130322", "160001", "194482", "234257", "279842", "331777", "390626", "456977", "531442", "614657", "707282", "810001", "923522", "1048577", "1185922", "1336337", "1500626", "1679617" ]
[ "nonn", "easy" ]
77
0
5
[ "A000404", "A002523", "A005117", "A111925" ]
null
N. J. A. Sloane
2024-01-26T04:41:03
oeisdata/seq/A002/A002523.seq
29b12b748da26681a90bf3370dd071f8
A002524
Number of permutations of length n within distance 2 of a fixed permutation.
[ "1", "1", "2", "6", "14", "31", "73", "172", "400", "932", "2177", "5081", "11854", "27662", "64554", "150639", "351521", "820296", "1914208", "4466904", "10423761", "24324417", "56762346", "132458006", "309097942", "721296815", "1683185225", "3927803988", "9165743600", "21388759708", "49911830577", "116471963129" ]
[ "nonn", "easy" ]
95
0
5
[ "A002524", "A306209" ]
[ "M1600", "N0626" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A002/A002524.seq
37d7a34bd3526326e15c557ba9c7e2d2
A002525
Number of permutations according to distance.
[ "0", "1", "2", "4", "10", "24", "55", "128", "300", "700", "1632", "3809", "8890", "20744", "48406", "112960", "263599", "615120", "1435416", "3349624", "7816528", "18240289", "42564706", "99327052", "231785058", "540883000", "1262179815", "2945365040", "6873169028", "16038912628" ]
[ "nonn" ]
55
0
5
[ "A002524", "A002525" ]
[ "M1203", "N0463" ]
N. J. A. Sloane
2022-01-22T16:26:42
oeisdata/seq/A002/A002525.seq
d3f1c974ea78dedf5bcc502d145b6ac7
A002526
Number of permutations of length n within distance 3 of a fixed permutation.
[ "1", "1", "2", "6", "24", "78", "230", "675", "2069", "6404", "19708", "60216", "183988", "563172", "1725349", "5284109", "16177694", "49526506", "151635752", "464286962", "1421566698", "4352505527", "13326304313", "40802053896", "124926806216", "382497958000", "1171122069784", "3585709284968", "10978628154457" ]
[ "nonn", "easy", "nice" ]
65
0
5
[ "A002524", "A002526", "A002527", "A002528", "A002529", "A188379", "A188491", "A188492", "A188493", "A188494", "A188495", "A188496", "A188497", "A188498", "A306209" ]
[ "M1671", "N0657" ]
N. J. A. Sloane
2025-01-05T19:51:32
oeisdata/seq/A002/A002526.seq
94684f5f2b941a92b5b8dbedd12c1647
A002527
Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(1) <= 3.
[ "0", "1", "2", "6", "18", "60", "184", "560", "1695", "5200", "15956", "48916", "149664", "458048", "1402360", "4294417", "13149210", "40259178", "123260854", "377395940", "1155508592", "3537919648", "10832298239", "33165996032", "101546731816", "310913195800", "951945967120", "2914642812096", "8923975209168" ]
[ "nonn" ]
52
0
5
null
[ "M1626", "N0637" ]
N. J. A. Sloane
2023-10-28T14:19:23
oeisdata/seq/A002/A002527.seq
870c8ea90b93436c21c5c1e1c2856c66
A002528
a(n) = A188491(n+1) - A188494(n) - A002526(n).
[ "0", "0", "2", "4", "12", "32", "108", "336", "1036", "3120", "9540", "29244", "89768", "274788", "840936", "2573972", "7881922", "24135000", "73897320", "226249264", "692714696", "2120941424", "6493883944", "19882820480", "60876609464", "186390208744", "570684661408", "1747307671896", "5349860697088" ]
[ "nonn", "easy" ]
37
0
5
null
[ "M1256", "N0480" ]
N. J. A. Sloane
2024-12-27T22:37:52
oeisdata/seq/A002/A002528.seq
4b32d198b6fad2a7209a0c5e133d5df6
A002529
a(n) = A002527(n+1) - A002527(n) - A002526(n).
[ "0", "0", "2", "6", "18", "46", "146", "460", "1436", "4352", "13252", "40532", "124396", "381140", "1166708", "3570684", "10932274", "33475170", "102499334", "313825690", "960844358", "2941873064", "9007393480", "27578681888", "84439657768", "258534813320", "791574775192", "2423623112104", "7420586212184", "22720153701768", "69563959091138" ]
[ "nonn", "easy" ]
40
0
5
null
[ "M1620", "N0633" ]
N. J. A. Sloane
2025-02-21T12:34:27
oeisdata/seq/A002/A002529.seq
7e10340c8144d92bd5a85ecadd7ec5a0
A002530
a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1.
[ "0", "1", "1", "3", "4", "11", "15", "41", "56", "153", "209", "571", "780", "2131", "2911", "7953", "10864", "29681", "40545", "110771", "151316", "413403", "564719", "1542841", "2107560", "5757961", "7865521", "21489003", "29354524", "80198051", "109552575", "299303201", "408855776", "1117014753", "1525870529", "4168755811" ]
[ "nonn", "easy", "frac", "core", "nice" ]
206
0
5
[ "A000129", "A001076", "A001353", "A001835", "A002530", "A002531", "A003297", "A005668", "A041007", "A041009", "A041011", "A041015", "A041017", "A042935", "A042937", "A048788", "A049310", "A108412", "A152063" ]
[ "M2363", "N0934" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002530.seq
a31b37dcbf564dfb9bb4b1d02567104a
A002531
a(2*n) = a(2*n-1) + a(2*n-2), a(2*n+1) = 2*a(2*n) + a(2*n-1); a(0) = a(1) = 1.
[ "1", "1", "2", "5", "7", "19", "26", "71", "97", "265", "362", "989", "1351", "3691", "5042", "13775", "18817", "51409", "70226", "191861", "262087", "716035", "978122", "2672279", "3650401", "9973081", "13623482", "37220045", "50843527", "138907099", "189750626", "518408351", "708158977", "1934726305" ]
[ "nonn", "frac", "easy", "core", "nice" ]
148
0
5
[ "A001075", "A001834", "A002316", "A002530", "A002531", "A026150", "A048788", "A053120", "A083332", "A199710" ]
[ "M1340", "N0513" ]
N. J. A. Sloane
2024-09-25T10:29:13
oeisdata/seq/A002/A002531.seq
dcd8a753a4813fb699c01a2cbc7b1fa5
A002532
a(n) = 2*a(n-1) + 5*a(n-2), a(0) = 0, a(1) = 1.
[ "0", "1", "2", "9", "28", "101", "342", "1189", "4088", "14121", "48682", "167969", "579348", "1998541", "6893822", "23780349", "82029808", "282961361", "976071762", "3366950329", "11614259468", "40063270581", "138197838502", "476712029909", "1644413252328", "5672386654201" ]
[ "nonn", "easy" ]
75
0
5
[ "A000129", "A001333", "A002532", "A002533", "A002605", "A015518", "A015519", "A015581", "A026150", "A046717", "A063727", "A083098", "A083099", "A083100", "A084057" ]
[ "M1923", "N0758" ]
N. J. A. Sloane
2022-09-08T08:44:30
oeisdata/seq/A002/A002532.seq
ac774f03dcc0bc4dee71207b3033e2d8
A002533
a(n) = 2*a(n-1) + 5*a(n-2), with a(0) = a(1) = 1.
[ "1", "1", "7", "19", "73", "241", "847", "2899", "10033", "34561", "119287", "411379", "1419193", "4895281", "16886527", "58249459", "200931553", "693110401", "2390878567", "8247309139", "28449011113", "98134567921", "338514191407", "1167701222419", "4027973401873", "13894452915841", "47928772841047", "165329810261299" ]
[ "nonn", "easy" ]
87
0
5
[ "A000129", "A001333", "A002532", "A002533", "A002605", "A015518", "A015519", "A026150", "A046717", "A063727", "A083098", "A083099", "A083100", "A084057" ]
[ "M4369", "N1834" ]
N. J. A. Sloane
2025-01-12T12:40:41
oeisdata/seq/A002/A002533.seq
3665d8f6c6e3090d321f03b87f5d32b8
A002534
a(n) = 2*a(n-1) + 9*a(n-2), with a(0) = 0, a(1) = 1.
[ "0", "1", "2", "13", "44", "205", "806", "3457", "14168", "59449", "246410", "1027861", "4273412", "17797573", "74055854", "308289865", "1283082416", "5340773617", "22229288978", "92525540509", "385114681820", "1602959228221", "6671950592822", "27770534239633", "115588623814664" ]
[ "nonn", "easy" ]
62
0
5
[ "A002534", "A015445", "A099012" ]
[ "M2058", "N0814" ]
N. J. A. Sloane
2024-01-04T09:11:51
oeisdata/seq/A002/A002534.seq
85217661cf4b8894e6ad90d20d504304
A002535
a(n) = 2*a(n-1) + 9*a(n-2), with a(0)=a(1)=1.
[ "1", "1", "11", "31", "161", "601", "2651", "10711", "45281", "186961", "781451", "3245551", "13524161", "56258281", "234234011", "974792551", "4057691201", "16888515361", "70296251531", "292589141311", "1217844546401", "5068991364601", "21098583646811", "87818089575031", "365523431971361", "1521409670118001", "6332530227978251" ]
[ "nonn", "easy" ]
60
0
5
[ "A002534", "A002535", "A011557", "A084132", "A098158", "A111015" ]
[ "M4786", "N2043" ]
N. J. A. Sloane
2023-01-29T06:01:58
oeisdata/seq/A002/A002535.seq
1dee9211fb1ff98f7f3f4dddb0824e01
A002536
a(n) = 8*a(n-2) - 9*a(n-4).
[ "0", "1", "1", "5", "8", "31", "55", "203", "368", "1345", "2449", "8933", "16280", "59359", "108199", "394475", "719072", "2621569", "4778785", "17422277", "31758632", "115784095", "211059991", "769472267", "1402652240", "5113721281", "9321678001", "33984519845", "61949553848", "225852667231" ]
[ "nonn", "easy" ]
48
0
5
null
[ "M3783", "N1540" ]
N. J. A. Sloane
2023-10-17T05:44:17
oeisdata/seq/A002/A002536.seq
cddec4499698f939d63c086b855c9da7
A002537
a(2n) = a(2n-1) + 3a(2n-2), a(2n+1) = 2a(2n) + 3a(2n-1).
[ "1", "1", "4", "11", "23", "79", "148", "533", "977", "3553", "6484", "23627", "43079", "157039", "286276", "1043669", "1902497", "6936001", "12643492", "46094987", "84025463", "306335887", "558412276", "2035832213", "3711069041", "13529634721", "24662841844", "89914587851" ]
[ "nonn" ]
36
0
5
null
[ "M3409", "N1379" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A002/A002537.seq
05ea8ca622933df58d89d72531affaaa
A002538
Second-order Eulerian numbers <<n+1,n-1>>.
[ "1", "8", "58", "444", "3708", "33984", "341136", "3733920", "44339040", "568356480", "7827719040", "115336085760", "1810992556800", "30196376985600", "532953524275200", "9927928075161600", "194677319705702400", "4008789120817152000", "86495828444928000000", "1951566265951948800000", "45958933902500720640000" ]
[ "nonn", "nice" ]
133
0
5
[ "A002538", "A008517", "A112007", "A121579" ]
[ "M4548", "N1932" ]
N. J. A. Sloane, Simon Plouffe, Mira Bernstein, Robert G. Wilson v
2024-12-27T08:48:31
oeisdata/seq/A002/A002538.seq
37ba957812ba759cd5353e513e2a987a
A002539
Eulerian numbers of the second kind: <<n+3, n>>.
[ "1", "22", "328", "4400", "58140", "785304", "11026296", "162186912", "2507481216", "40788301824", "697929436800", "12550904017920", "236908271543040", "4687098165573120", "97049168010017280", "2099830209402931200", "47405948832458496000", "1115089078488795648000", "27290469545695931904000", "694002594415741341696000" ]
[ "nonn", "nice", "easy" ]
61
0
5
[ "A002539", "A008517", "A112007" ]
[ "M5126", "N2221" ]
N. J. A. Sloane , Simon Plouffe, Robert G. Wilson v, Mira Bernstein
2018-08-11T02:55:20
oeisdata/seq/A002/A002539.seq
873f6cf10dbccf5ad18b331f7591bb0c
A002540
Increasing gaps between prime-powers.
[ "1", "5", "13", "19", "32", "53", "89", "139", "199", "293", "887", "1129", "1331", "5591", "8467", "9551", "15683", "19609", "31397", "155921", "360653", "370261", "492113", "1349533", "1357201", "2010733", "4652353", "17051707", "20831323", "47326693", "122164747", "189695659", "191912783", "387096133", "436273009", "1294268491" ]
[ "nonn", "nice" ]
55
0
5
[ "A000961", "A002386", "A002540", "A057820", "A094158", "A121493" ]
[ "M1431", "N0565" ]
N. J. A. Sloane
2024-10-18T08:58:38
oeisdata/seq/A002/A002540.seq
3ae2c979deeea30fbbf3ed5712cdf844
A002541
a(n) = Sum_{k=1..n-1} floor((n-k)/k).
[ "0", "1", "2", "4", "5", "8", "9", "12", "14", "17", "18", "23", "24", "27", "30", "34", "35", "40", "41", "46", "49", "52", "53", "60", "62", "65", "68", "73", "74", "81", "82", "87", "90", "93", "96", "104", "105", "108", "111", "118", "119", "126", "127", "132", "137", "140", "141", "150", "152", "157", "160", "165", "166", "173", "176", "183", "186", "189", "190", "201", "202", "205" ]
[ "nonn", "easy", "nice" ]
101
0
5
[ "A000005", "A002541", "A003238", "A003988", "A004199", "A006218", "A020639", "A027749", "A032741", "A070776", "A126656", "A320224", "A320225", "A320226" ]
[ "M0970", "N0362" ]
N. J. A. Sloane
2024-07-31T09:21:54
oeisdata/seq/A002/A002541.seq
9b9c969b1baa4886bd6285b38022d5c9
A002542
Number of two-valued complete Post functions of n variables.
[ "0", "2", "56", "16256", "1073709056", "4611686016279904256", "85070591730234615856620279821087277056", "28948022309329048855892746252171976963147354982949671778132708698262398304256" ]
[ "nonn" ]
37
0
5
[ "A002542", "A002543" ]
[ "M2174", "N0869" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002542.seq
374768420a31d44ac34273b9da338f11
A002543
Complete Post functions of n variables.
[ "0", "2", "16", "980", "9332768" ]
[ "nonn", "more" ]
30
0
5
[ "A002542", "A002543", "A002857" ]
[ "M2098", "N0830" ]
N. J. A. Sloane
2023-10-16T23:47:32
oeisdata/seq/A002/A002543.seq
cffe2f4c10ac2cfbb18d9523bd3812dc
A002544
a(n) = binomial(2*n+1,n)*(n+1)^2.
[ "1", "12", "90", "560", "3150", "16632", "84084", "411840", "1969110", "9237800", "42678636", "194699232", "878850700", "3931426800", "17450721000", "76938289920", "337206098790", "1470171918600", "6379820115900", "27569305764000", "118685861314020", "509191949220240", "2177742427450200", "9287309860732800" ]
[ "nonn", "easy", "nice" ]
125
0
5
[ "A002457", "A002544", "A002674", "A002736", "A085373", "A202543", "A331430" ]
[ "M4855", "N2075" ]
N. J. A. Sloane, Simon Plouffe
2022-10-18T19:10:58
oeisdata/seq/A002/A002544.seq
a7b38ee9037ebe97ffe43e36c441e6c7
A002545
Numerator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).
[ "1", "3", "7", "15", "29", "469", "29531", "1303", "16103", "190553", "128977", "9061", "30946717", "39646461", "58433327", "344499373", "784809203", "169704792667", "665690574539", "5667696059", "337284946763", "7964656853269", "46951444927823", "284451446729", "1597747168263479", "816088653136373" ]
[ "nonn", "frac" ]
42
0
5
[ "A002545", "A002546" ]
[ "M2651", "N1058" ]
N. J. A. Sloane
2018-11-17T20:45:11
oeisdata/seq/A002/A002545.seq
bace7b883cdec811576e9d84b94063aa
A002546
Denominator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).
[ "1", "2", "4", "8", "15", "240", "15120", "672", "8400", "100800", "69300", "4950", "17199000", "22422400", "33633600", "201801600", "467812800", "102918816000", "410646075840", "3555377280", "215100325440", "5162407810560", "30920671782000", "190281057120", "1085315579548200", "562756226432400", "22969641895200" ]
[ "nonn", "frac" ]
29
0
5
[ "A002545", "A002546" ]
[ "M1110", "N0424" ]
N. J. A. Sloane
2018-11-17T21:31:11
oeisdata/seq/A002/A002546.seq
72871e792f283202737fc72071984deb
A002547
Numerator of the n-th harmonic number H(n) divided by (n+1); a(n) = A001008(n) / ((n+1)*A002805(n)).
[ "1", "1", "11", "5", "137", "7", "363", "761", "7129", "671", "83711", "6617", "1145993", "1171733", "1195757", "143327", "42142223", "751279", "275295799", "55835135", "18858053", "830139", "444316699", "269564591", "34052522467", "34395742267", "312536252003", "10876020307", "9227046511387", "300151059037" ]
[ "nonn", "frac" ]
79
0
5
[ "A001008", "A002547", "A002548", "A002805" ]
[ "M4765", "N2036" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002547.seq
5847623bb1bc53678dac311bdbe4cce7
A002548
Denominators of coefficients for numerical differentiation.
[ "1", "1", "12", "6", "180", "10", "560", "1260", "12600", "1260", "166320", "13860", "2522520", "2702700", "2882880", "360360", "110270160", "2042040", "775975200", "162954792", "56904848", "2586584", "1427794368", "892371480", "116008292400", "120470149800", "1124388064800" ]
[ "nonn", "frac" ]
57
0
5
[ "A002547", "A002548", "A093762" ]
[ "M4822", "N2063" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002548.seq
7ec594ac727e01304bdeb3ede4bf8fc7
A002549
Numerators of coefficients of log(1+x)/sqrt(1+x).
[ "1", "1", "23", "11", "563", "1627", "88069", "1423", "1593269", "7759469", "31730711", "46522243", "3788707301", "2888008157", "340028535787", "41743955887", "10823198495797", "2738032559863", "409741429887649", "25876414060339", "17141894231615609" ]
[ "nonn", "frac" ]
34
0
5
[ "A002428", "A002549", "A002550" ]
[ "M5128", "N2223" ]
N. J. A. Sloane
2015-07-18T13:15:38
oeisdata/seq/A002/A002549.seq
fb7741b39a67d712de7904e00ffe6470
A002550
Denominators of coefficients of log(1+x)/sqrt(1+x).
[ "1", "1", "24", "12", "640", "1920", "107520", "1792", "2064384", "10321920", "43253760", "64880640", "5398069248", "4198498304", "503819796480", "62977474560", "16610786017280", "4271344975872", "649244436332544", "41618233098240", "27967452642017280" ]
[ "nonn", "frac" ]
24
0
5
[ "A002549", "A002550" ]
[ "M5139", "N2229" ]
N. J. A. Sloane
2023-10-16T23:49:00
oeisdata/seq/A002/A002550.seq
55715f16e4a19b1c53b911dfe90f1344
A002551
Numerators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).
[ "0", "1", "-3", "43", "-95", "12139", "-25333", "81227", "-498233", "121563469", "-246183839", "32808117961", "-13219717433", "3226018634857", "-8835766426243", "390013167515221", "-260612031438103", "36514732926665911", "-73104960503491573", "9265088297941326563", "-389193444786378151123" ]
[ "sign", "frac" ]
29
0
5
[ "A002551", "A002552" ]
[ "M3151", "N1276" ]
N. J. A. Sloane
2023-10-16T23:50:02
oeisdata/seq/A002/A002551.seq
c4d191237f11d0018980312ef4ad9a2a
A002552
Denominators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).
[ "1", "1", "2", "24", "48", "5760", "11520", "35840", "215040", "51609600", "103219200", "13624934400", "5449973760", "1322526965760", "3606891724800", "158703235891200", "105802157260800", "14800210341396480", "29600420682792960", "3749386619820441600" ]
[ "nonn", "frac" ]
23
0
5
[ "A002551", "A002552" ]
[ "M2133", "N0846" ]
N. J. A. Sloane
2023-10-16T23:50:51
oeisdata/seq/A002/A002552.seq
55c1579697e964ced02fc1c43980b7a1
A002553
Coefficients for numerical differentiation.
[ "1", "24", "640", "7168", "294912", "2883584", "54525952", "167772160", "36507222016", "326417514496", "5772436045824", "50577534877696", "1759218604441600", "15199648742375424", "261208778387488768", "2233785415175766016", "101457092405402533888" ]
[ "nonn" ]
31
0
5
[ "A001818", "A002553", "A002555" ]
[ "M5166", "N2243" ]
N. J. A. Sloane
2015-07-18T13:17:00
oeisdata/seq/A002/A002553.seq
56c3ee748b7814d37274b4c2c56b3989
A002554
Numerators of coefficients for numerical differentiation.
[ "1", "-5", "259", "-3229", "117469", "-7156487", "2430898831", "-60997921", "141433003757", "-25587296781661", "51270597630767", "-6791120985104747", "3400039831130408821", "-15317460638921852507", "25789165074168004597399", "-1550286106708510672406629", "24823277118070193095631689" ]
[ "sign", "frac" ]
41
0
5
[ "A001824", "A002554", "A002555" ]
[ "M4034", "N1676" ]
N. J. A. Sloane
2023-10-15T09:27:53
oeisdata/seq/A002/A002554.seq
68f47418b93e16c55a5f368115022920
A002555
Denominators of coefficients for numerical differentiation.
[ "1", "24", "5760", "322560", "51609600", "13624934400", "19837904486400", "2116043145216", "20720294477955072", "15747423803245854720", "131978409017679544320", "72852081777759108464640", "151532330097738945606451200", "2828603495157793651320422400", "19687080326298243813190139904000" ]
[ "nonn", "frac" ]
32
0
5
[ "A001824", "A002554", "A002555" ]
[ "M5177", "N2249" ]
N. J. A. Sloane
2019-02-27T14:03:01
oeisdata/seq/A002/A002555.seq
e0888601b0cdb2e65aa16bda714b66f5
A002556
Odd squarefree numbers with an odd number of prime factors that have no prime factors greater than 31.
[ "3", "5", "7", "11", "13", "17", "19", "23", "29", "31", "105", "165", "195", "231", "255", "273", "285", "345", "357", "385", "399", "429", "435", "455", "465", "483", "561", "595", "609", "627", "651", "663", "665", "715", "741", "759", "805", "897", "935", "957", "969", "1001", "1015", "1023", "1045", "1085", "1105", "1131", "1173", "1209", "1235", "1265" ]
[ "nonn", "fini", "full" ]
40
0
5
[ "A002556", "A002557", "A056912", "A067019" ]
[ "M2412", "N0955" ]
N. J. A. Sloane, Oct 07 2015
2022-09-08T08:44:31
oeisdata/seq/A002/A002556.seq
590c3d24350366429eb21c86ed62ae47
A002557
Odd squarefree numbers with an even number of prime factors that have no prime factors greater than 31.
[ "1", "15", "21", "33", "35", "39", "51", "55", "57", "65", "69", "77", "85", "87", "91", "93", "95", "115", "119", "133", "143", "145", "155", "161", "187", "203", "209", "217", "221", "247", "253", "299", "319", "323", "341", "377", "391", "403", "437", "493", "527", "551", "589", "667", "713", "899", "1155", "1365", "1785", "1995", "2145", "2415", "2805", "3003" ]
[ "nonn", "full", "fini" ]
41
0
5
[ "A002556", "A002557", "A046337", "A056913", "A059897" ]
[ "M4959", "N2126" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002557.seq
2ccbd583538672bbb4809e6b4ba30565
A002558
Coefficients of a Dirichlet series.
[ "1", "-1", "4", "-3", "-4", "-4", "8", "11", "4", "4", "12", "-48", "-12", "-8", "-16", "25", "-16", "-4", "20", "0", "32", "-12", "24", "248", "-4", "12", "4", "-208", "-28", "16", "32", "-41", "48", "16", "-32", "-400", "-36", "-20", "-48", "88", "-40", "-32", "44", "-544", "-16", "-24", "48", "732", "8", "4" ]
[ "sign" ]
21
0
5
null
[ "M3211", "N1300" ]
N. J. A. Sloane
2023-10-16T23:51:59
oeisdata/seq/A002/A002558.seq
7a6abcc1c917b7b324203a2d3742cc15
A002559
Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.
[ "1", "2", "5", "13", "29", "34", "89", "169", "194", "233", "433", "610", "985", "1325", "1597", "2897", "4181", "5741", "6466", "7561", "9077", "10946", "14701", "28657", "33461", "37666", "43261", "51641", "62210", "75025", "96557", "135137", "195025", "196418", "294685", "426389", "499393", "514229", "646018", "925765", "1136689", "1278818" ]
[ "nonn", "nice", "easy" ]
218
0
5
[ "A000045", "A001653", "A002559", "A004280", "A158381", "A158384", "A178444", "A256395" ]
[ "M1432", "N0566" ]
N. J. A. Sloane and J. H. Conway
2025-01-05T19:51:32
oeisdata/seq/A002/A002559.seq
0941322a31ac4c7075ba5d74a306caf2
A002560
Number of polygonal graphs.
[ "1", "1", "4", "2", "7", "5", "15", "6", "37", "13", "36", "32", "37", "34", "73", "58", "183", "150", "262", "186", "1009", "420", "707", "703", "760", "1180", "4639" ]
[ "nonn", "more" ]
28
0
5
null
[ "M3203", "N1295" ]
N. J. A. Sloane
2023-10-16T23:52:38
oeisdata/seq/A002/A002560.seq
a0b6b9b9b3b5ec2a359bdaa10f526c48
A002561
a(n) = n^5 + 1.
[ "0", "1", "2", "33", "244", "1025", "3126", "7777", "16808", "32769", "59050", "100001", "161052", "248833", "371294", "537825", "759376", "1048577", "1419858", "1889569", "2476100", "3200001", "4084102", "5153633", "6436344", "7962625", "9765626", "11881377", "14348908", "17210369", "20511150", "24300001", "28629152", "33554433" ]
[ "nonn", "easy" ]
64
0
5
[ "A000584", "A002561" ]
null
N. J. A. Sloane
2024-02-26T20:11:20
oeisdata/seq/A002/A002561.seq
476af1a52bf465a1cfe7643313e99f8c
A002562
Number of ways of placing n nonattacking queens on n X n board (symmetric solutions count only once).
[ "1", "0", "0", "1", "2", "1", "6", "12", "46", "92", "341", "1787", "9233", "45752", "285053", "1846955", "11977939", "83263591", "621012754", "4878666808", "39333324973", "336376244042", "3029242658210", "28439272956934", "275986683743434", "2789712466510289", "29363495934315694" ]
[ "nonn", "nice" ]
78
0
5
[ "A000170", "A002562", "A032522", "A033148" ]
[ "M0180", "N0068" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002562.seq
d5461d61c4fb72664a7df25ee0ceeb59
A002563
Number of nonisomorphic solutions to minimal dominating set on queens' graph Q(n).
[ "1", "1", "1", "3", "37", "1", "13", "638", "21", "1", "1", "1", "41", "588", "25872", "43", "22", "2" ]
[ "nonn", "more" ]
25
0
5
[ "A002563", "A002564", "A075458" ]
[ "M3142", "N1273" ]
N. J. A. Sloane
2021-09-02T14:08:51
oeisdata/seq/A002/A002563.seq
47b98c85ef5b7be3464e846e10d38319
A002564
Number of different ways one can attack all squares on an n X n chessboard using the minimum number of queens.
[ "1", "4", "1", "12", "186", "4", "86", "4860", "114", "8", "2", "8", "288", "4632", "205832", "2968", "124", "16", "84" ]
[ "nonn", "more", "changed" ]
99
0
5
[ "A002563", "A002564", "A002568", "A075458", "A182333", "A286883" ]
[ "M3199", "N1293" ]
N. J. A. Sloane
2025-04-14T09:07:57
oeisdata/seq/A002/A002564.seq
b6c075b4e5dbc8b14caa1e751f878208
A002565
Number of non-isomorphic ways to attack all squares on an n X n chessboard using the smallest possible number of queens with each queen attacking at least one other.
[ "0", "2", "5", "3", "15", "150", "5", "56", "3", "39", "681" ]
[ "nonn", "more" ]
29
0
5
[ "A002565", "A002566" ]
[ "M1313", "N0502" ]
N. J. A. Sloane
2017-12-25T11:58:13
oeisdata/seq/A002/A002565.seq
df727107221062e07b8d7dd469485778
A002566
Number of ways to attack all squares on an n X n chessboard using the smallest possible number of queens with each queen attacking at least one other.
[ "0", "6", "20", "12", "70", "960", "22", "352", "10", "216", "4814", "72" ]
[ "nonn", "hard", "more" ]
38
0
5
[ "A002565", "A002566" ]
[ "M4130", "N1713" ]
N. J. A. Sloane
2025-04-05T08:34:37
oeisdata/seq/A002/A002566.seq
f0cf593437f147cd23287a784e6bb396
A002567
Number of nonisomorphic solutions to minimal independent dominating set on queens' graph Q(n).
[ "1", "1", "1", "2", "2", "17", "1", "91", "16", "1", "1", "105", "4", "55", "1314", "16", "2", "28" ]
[ "nonn", "more" ]
24
0
5
[ "A002567", "A002568", "A075324" ]
[ "M0389", "N0147" ]
N. J. A. Sloane
2023-10-16T23:53:35
oeisdata/seq/A002/A002567.seq
a70601a9fef4f113c155ccdaa977a85f
A002568
Number of different ways one can attack all squares on an n X n chessboard with the smallest number of non-attacking queens needed.
[ "1", "4", "1", "16", "16", "120", "8", "728", "92", "8", "2", "840", "24", "436", "10188", "128", "12", "224", "8424", "312", "72", "192", "8784", "368", "56", "224", "14500", "280", "10880", "240" ]
[ "nonn", "hard", "more" ]
38
0
5
[ "A002564", "A002567", "A002568", "A103315", "A122749" ]
[ "M3200", "N1294" ]
N. J. A. Sloane
2024-10-04T10:04:12
oeisdata/seq/A002/A002568.seq
3385530a1110c3518c24e103d9a87822
A002569
Max_{k=0..n} { Number of partitions of n into exactly k parts }.
[ "1", "1", "1", "1", "2", "2", "3", "4", "5", "7", "9", "11", "15", "18", "23", "30", "37", "47", "58", "71", "90", "110", "136", "164", "201", "248", "300", "364", "436", "525", "638", "764", "919", "1090", "1297", "1549", "1845", "2194", "2592", "3060", "3590", "4242", "5013", "5888", "6912", "8070", "9418", "11004", "12866", "15021", "17475", "20298", "23501", "27169" ]
[ "nonn" ]
68
0
5
[ "A000041", "A002569", "A008284", "A026819", "A046155" ]
[ "M0283", "N0101" ]
N. J. A. Sloane
2017-10-22T22:08:25
oeisdata/seq/A002/A002569.seq
493a7e46a7dc33d36078870c47cffae7
A002570
From a definite integral.
[ "1", "1", "6", "11", "36", "85", "235", "600", "1590", "4140", "10866", "28416", "74431", "194821", "510096", "1335395", "3496170", "9153025", "23963005", "62735880", "164244756", "429998256", "1125750156", "2947252056", "7716006181", "20200766305", "52886292930", "138458112275", "362488044120" ]
[ "nonn" ]
43
0
5
null
[ "M4090", "N1698" ]
N. J. A. Sloane
2024-07-31T04:10:07
oeisdata/seq/A002/A002570.seq
18fa109671063feb6c239b05079e3be2
A002571
From a definite integral.
[ "1", "5", "10", "30", "74", "199", "515", "1355", "3540", "9276", "24276", "63565", "166405", "435665", "1140574", "2986074", "7817630", "20466835", "53582855", "140281751", "367262376", "961505400", "2517253800", "6590256025", "17253514249", "45170286749", "118257345970" ]
[ "nonn" ]
58
0
5
[ "A000045", "A000204", "A001654", "A002571", "A006206", "A064831", "A077916", "A180662" ]
[ "M3802", "N1553" ]
N. J. A. Sloane
2023-08-05T13:09:26
oeisdata/seq/A002/A002571.seq
3e1f83e8e2d63a73a0a39a5c9541038c
A002572
Number of partitions of 1 into n powers of 1/2; or (according to one definition of "binary") the number of binary rooted trees.
[ "1", "1", "1", "2", "3", "5", "9", "16", "28", "50", "89", "159", "285", "510", "914", "1639", "2938", "5269", "9451", "16952", "30410", "54555", "97871", "175586", "315016", "565168", "1013976", "1819198", "3263875", "5855833", "10506175", "18849555", "33818794", "60675786", "108861148", "195312750", "350419594", "628704034", "1127987211", "2023774607", "3630948907" ]
[ "core", "nonn", "nice", "easy" ]
122
0
5
[ "A002572", "A002573", "A002574", "A007178", "A047913", "A049284", "A049285", "A102375", "A294775" ]
[ "M0710", "N0261" ]
N. J. A. Sloane
2022-01-15T00:26:37
oeisdata/seq/A002/A002572.seq
ad72b1507d939fefd023fc17a929c3da
A002573
Restricted partitions.
[ "0", "1", "1", "2", "4", "7", "12", "22", "39", "70", "126", "225", "404", "725", "1299", "2331", "4182", "7501", "13458", "24145", "43316", "77715", "139430", "250152", "448808", "805222", "1444677", "2591958", "4650342", "8343380", "14969239", "26856992", "48185362", "86451602", "155106844", "278284440", "499283177", "895787396", "1607174300", "2883507098" ]
[ "nonn", "easy" ]
32
0
5
[ "A002572", "A002573", "A002574", "A047913", "A049284", "A049285", "A176431" ]
[ "M1062", "N0399" ]
N. J. A. Sloane
2021-12-20T20:22:22
oeisdata/seq/A002/A002573.seq
13680bf5a9e9c06eb1a9b7a540de4ede
A002574
Restricted partitions.
[ "0", "0", "1", "1", "2", "4", "7", "13", "24", "42", "76", "137", "245", "441", "792", "1420", "2550", "4576", "8209", "14732", "26433", "47424", "85092", "152670", "273914", "491453", "881744", "1581985", "2838333", "5092398", "9136528", "16392311", "29410243", "52766343", "94670652", "169853138", "304741614", "546751437", "980952673", "1759973660" ]
[ "nonn", "easy" ]
32
0
5
[ "A002572", "A002573", "A002574", "A047913", "A049284", "A049285" ]
[ "M1070", "N0404" ]
N. J. A. Sloane
2023-10-17T05:26:00
oeisdata/seq/A002/A002574.seq
8455a00139af3f4ffec0fe0847c40440
A002575
Coefficients of Bell's formula for making change.
[ "1", "3", "9", "35", "201", "1827", "27337", "692003", "30251721", "2320518947", "316359580361", "77477180493603", "34394869942983369", "27893897106768940835", "41603705003444309596873", "114788185359199234852802339", "588880400923055731115178072777" ]
[ "nonn" ]
25
0
5
[ "A002575", "A002576", "A002577", "A125792", "A262554" ]
[ "M2820", "N1134" ]
N. J. A. Sloane
2023-03-22T21:57:38
oeisdata/seq/A002/A002575.seq
e2b34dc9a58e07e5e5862d59a6cd5189
A002576
Coefficients of Bell's formula for making change.
[ "2", "16", "130", "1424", "23682", "637328", "28867714", "2260015504", "311718542466", "76844461332880", "34239915581996162", "27825107366882974096", "41547917209230771715202", "114704977949192346233608592", "588650824552337332645472468098" ]
[ "nonn" ]
19
0
5
[ "A002575", "A002576", "A002577", "A262554" ]
[ "M2091", "N0826" ]
N. J. A. Sloane
2023-10-16T23:58:10
oeisdata/seq/A002/A002576.seq
c2e1f79409fbc5da81c8b3db5d5247db
A002577
Number of partitions of 2^n into powers of 2.
[ "1", "2", "4", "10", "36", "202", "1828", "27338", "692004", "30251722", "2320518948", "316359580362", "77477180493604", "34394869942983370", "27893897106768940836", "41603705003444309596874", "114788185359199234852802340", "588880400923055731115178072778", "5642645813427132737155703265972004" ]
[ "nonn", "easy", "nice" ]
87
0
5
[ "A000079", "A000123", "A000290", "A000447", "A002575", "A002576", "A002577", "A018818", "A078121", "A078125", "A078537", "A125790", "A145513", "A145515", "A152977" ]
[ "M1239", "N0473" ]
N. J. A. Sloane
2024-07-31T09:02:17
oeisdata/seq/A002/A002577.seq
61643426add5a6a88cca59c7a6c9f4ba
A002578
Number of integral points in a certain sequence of open quadrilaterals.
[ "0", "0", "1", "3", "6", "9", "13", "18", "24", "31", "39", "47", "56", "66", "77", "89", "102", "115", "129", "144", "160", "177", "195", "213", "232", "252", "273", "295", "318", "341", "365", "390", "416", "443", "471", "499", "528", "558", "589", "621", "654", "687", "721", "756", "792", "829", "867", "905", "944", "984", "1025", "1067", "1110" ]
[ "nonn", "easy" ]
38
0
5
[ "A002578", "A002579" ]
[ "M2529", "N0997" ]
N. J. A. Sloane
2024-05-02T09:47:05
oeisdata/seq/A002/A002578.seq
833286773d405133f83b47036b3a398d
A002579
Number of integral points in a certain sequence of closed quadrilaterals.
[ "3", "5", "8", "12", "17", "23", "30", "37", "45", "54", "64", "75", "87", "99", "112", "126", "141", "157", "174", "191", "209", "228", "248", "269", "291", "313", "336", "360", "385", "411", "438", "465", "493", "522", "552", "583", "615", "647", "680", "714", "749", "785", "822", "859", "897", "936", "976", "1017", "1059", "1101", "1144" ]
[ "nonn", "easy" ]
30
0
5
[ "A002578", "A002579" ]
[ "M2440", "N0967" ]
N. J. A. Sloane
2024-05-02T04:31:59
oeisdata/seq/A002/A002579.seq
b5c0cd5334e1cdc7dc6aebfe8e0a4eb4
A002580
Decimal expansion of cube root of 2.
[ "1", "2", "5", "9", "9", "2", "1", "0", "4", "9", "8", "9", "4", "8", "7", "3", "1", "6", "4", "7", "6", "7", "2", "1", "0", "6", "0", "7", "2", "7", "8", "2", "2", "8", "3", "5", "0", "5", "7", "0", "2", "5", "1", "4", "6", "4", "7", "0", "1", "5", "0", "7", "9", "8", "0", "0", "8", "1", "9", "7", "5", "1", "1", "2", "1", "5", "5", "2", "9", "9", "6", "7", "6", "5", "1", "3", "9", "5", "9", "4", "8", "3", "7", "2", "9", "3", "9", "6", "5", "6", "2", "4", "3", "6", "2", "5", "5", "0", "9", "4", "1", "5", "4", "3", "1", "0", "2", "5" ]
[ "nonn", "easy", "cons" ]
115
0
5
[ "A002580", "A002581", "A002945", "A005480", "A005481", "A005482", "A005486", "A010581", "A010582", "A092039", "A092041", "A139340", "A246644", "A253583", "A270714" ]
[ "M1354", "N0521" ]
N. J. A. Sloane
2025-03-16T08:17:26
oeisdata/seq/A002/A002580.seq
b097f85b54763636d27607366f0db794
A002581
Decimal expansion of cube root of 3.
[ "1", "4", "4", "2", "2", "4", "9", "5", "7", "0", "3", "0", "7", "4", "0", "8", "3", "8", "2", "3", "2", "1", "6", "3", "8", "3", "1", "0", "7", "8", "0", "1", "0", "9", "5", "8", "8", "3", "9", "1", "8", "6", "9", "2", "5", "3", "4", "9", "9", "3", "5", "0", "5", "7", "7", "5", "4", "6", "4", "1", "6", "1", "9", "4", "5", "4", "1", "6", "8", "7", "5", "9", "6", "8", "2", "9", "9", "9", "7", "3", "3", "9", "8", "5", "4", "7", "5", "5", "4", "7", "9", "7", "0", "5", "6", "4", "5", "2", "5", "6", "6", "8", "6", "8", "3", "5", "0", "8" ]
[ "nonn", "cons" ]
64
0
5
[ "A002581", "A002946" ]
[ "M3220", "N1304" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002581.seq
67c113dcaf596f29353a68f1194db28b
A002582
Largest prime factor of n! - 1.
[ "1", "5", "23", "17", "719", "5039", "1753", "2999", "125131", "7853", "479001599", "3593203", "87178291199", "1510259", "6880233439", "256443711677", "478749547", "78143369", "19499250680671", "4826713612027", "170006681813", "498390560021687969", "991459181683", "114776274341482621993" ]
[ "nonn", "nice" ]
51
0
5
[ "A002582", "A002583", "A033312", "A054415", "A056110" ]
[ "M3925", "N1613" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002582.seq
fad84370187b97b3054e5fb634abdef4
A002583
Largest prime factor of n! + 1.
[ "2", "2", "3", "7", "5", "11", "103", "71", "661", "269", "329891", "39916801", "2834329", "75024347", "3790360487", "46271341", "1059511", "1000357", "123610951", "1713311273363831", "117876683047", "2703875815783", "93799610095769647", "148139754736864591", "765041185860961084291", "38681321803817920159601" ]
[ "nonn", "nice" ]
58
0
5
[ "A002582", "A002583", "A002981", "A038507", "A051301", "A056111", "A096225" ]
[ "M0294", "N0312" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002583.seq
ced5172fdc4f1976266231c2e4948def
A002584
Largest prime factor of product of first n primes - 1, or 1 if no such prime exists.
[ "1", "5", "29", "19", "2309", "30029", "8369", "929", "46027", "81894851", "876817", "38669", "304250263527209", "92608862041", "59799107", "1143707681", "69664915493", "1146665184811", "17975352936245519", "2140320249725509" ]
[ "nonn", "nice" ]
55
0
5
[ "A002110", "A002584", "A002585", "A006530", "A057588" ]
[ "M3952", "N1628" ]
N. J. A. Sloane
2020-02-13T11:57:10
oeisdata/seq/A002/A002584.seq
4fcdc0cfc08cda408f8866cb496bd6eb
A002585
Largest prime factor of 1 + (product of first n primes).
[ "3", "7", "31", "211", "2311", "509", "277", "27953", "703763", "34231", "200560490131", "676421", "11072701", "78339888213593", "13808181181", "18564761860301", "19026377261", "525956867082542470777", "143581524529603", "2892214489673", "16156160491570418147806951", "96888414202798247", "1004988035964897329167431269" ]
[ "nonn", "nice" ]
69
0
5
[ "A002110", "A002584", "A002585", "A006530", "A006862", "A051342" ]
[ "M2697", "N1081" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002585.seq
07990a743f7f635a7d7d5495bbc9563b
A002586
Smallest prime factor of 2^n + 1.
[ "3", "5", "3", "17", "3", "5", "3", "257", "3", "5", "3", "17", "3", "5", "3", "65537", "3", "5", "3", "17", "3", "5", "3", "97", "3", "5", "3", "17", "3", "5", "3", "641", "3", "5", "3", "17", "3", "5", "3", "257", "3", "5", "3", "17", "3", "5", "3", "193", "3", "5", "3", "17", "3", "5", "3", "257", "3", "5", "3", "17", "3", "5", "3", "274177", "3", "5", "3", "17", "3", "5", "3", "97", "3", "5", "3", "17", "3", "5", "3", "65537", "3", "5", "3", "17", "3", "5" ]
[ "nonn", "nice" ]
77
0
5
[ "A000215", "A001269", "A002586", "A002587", "A019434", "A050922", "A093179" ]
[ "M2385", "N0947" ]
N. J. A. Sloane
2024-12-30T02:18:54
oeisdata/seq/A002/A002586.seq
5116cc9d75975175e35dfb5cc135a418
A002587
Largest prime factor of 2^n + 1.
[ "2", "3", "5", "3", "17", "11", "13", "43", "257", "19", "41", "683", "241", "2731", "113", "331", "65537", "43691", "109", "174763", "61681", "5419", "2113", "2796203", "673", "4051", "1613", "87211", "15790321", "3033169", "1321", "715827883", "6700417", "20857", "26317", "86171", "38737", "25781083", "525313" ]
[ "nonn" ]
113
0
5
[ "A000051", "A002586", "A002587", "A006530", "A274903" ]
[ "M2386", "N0948" ]
N. J. A. Sloane
2025-03-15T13:48:17
oeisdata/seq/A002/A002587.seq
2ff01eb7bc7bdbc4a7ec97b40e6fda52
A002588
a(n) = largest noncomposite factor of 2^(2n+1) - 1.
[ "1", "7", "31", "127", "73", "89", "8191", "151", "131071", "524287", "337", "178481", "1801", "262657", "2089", "2147483647", "599479", "122921", "616318177", "121369", "164511353", "2099863", "23311", "13264529", "4432676798593", "131071", "20394401", "201961", "1212847", "3203431780337" ]
[ "nonn" ]
55
0
5
[ "A002184", "A002588", "A005420", "A147590" ]
[ "M4401", "N1856" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002588.seq
6755ee2b42efe4b671377d4c14ac4938
A002589
Largest primitive factor of 2^(2n+1) + 1.
[ "3", "1", "11", "43", "19", "683", "2731", "331", "43691", "174763", "5419", "2796203", "4051", "87211", "3033169", "715827883", "20857", "86171", "25781083", "22366891", "8831418697", "2932031007403", "18837001", "165768537521", "4363953127297", "6529", "28059810762433", "48912491", "160465489" ]
[ "nonn" ]
44
0
5
null
[ "M2234", "N0886" ]
N. J. A. Sloane
2025-02-25T23:22:13
oeisdata/seq/A002/A002589.seq
19cd2f37ba17037321ea9ef0b4f683c7
A002590
Largest prime factor of 16^n + 1.
[ "2", "17", "257", "241", "65537", "61681", "673", "15790321", "6700417", "38737", "4278255361", "2931542417", "22253377", "308761441", "54410972897", "4562284561", "67280421310721", "2879347902817", "487824887233", "24517014940753", "44479210368001", "88959882481" ]
[ "nonn" ]
71
0
5
null
[ "M5046", "N2180" ]
N. J. A. Sloane
2025-03-15T13:49:44
oeisdata/seq/A002/A002590.seq
85c28cda9ec8836392e27fcdd510f3cd
A002591
Largest prime factor of 3^(2n+1) - 1.
[ "2", "13", "11", "1093", "757", "3851", "797161", "4561", "34511", "363889", "368089", "1001523179", "391151", "8209", "20381027", "4404047", "2413941289", "2664097031", "17189128703", "797161", "86950696619", "380808546861411923", "927001", "96656723", "131713", "99810171997" ]
[ "nonn" ]
47
0
5
[ "A002591", "A057958", "A059885", "A074477", "A085028", "A133801", "A235366", "A274909" ]
[ "M4886", "N2095" ]
N. J. A. Sloane
2022-10-19T09:16:24
oeisdata/seq/A002/A002591.seq
e4dd6c4d4c550c3c4857c819ae659666
A002592
Largest prime factor of 9^n + 1.
[ "2", "5", "41", "73", "193", "1181", "6481", "16493", "21523361", "530713", "42521761", "570461", "769", "4795973261", "647753", "47763361", "926510094425921", "1743831169", "282429005041", "25480398173", "128653413121", "109688713", "56625998353", "70601370627701" ]
[ "nonn" ]
46
0
5
[ "A002592", "A006530", "A062396", "A274903", "A274909" ]
[ "M3994", "N1655" ]
N. J. A. Sloane
2022-09-08T08:44:31
oeisdata/seq/A002/A002592.seq
ad612af9be672e4c0f12cb9596901d47
A002593
a(n) = n^2*(2*n^2 - 1); also Sum_{k=0..n-1} (2k+1)^3.
[ "0", "1", "28", "153", "496", "1225", "2556", "4753", "8128", "13041", "19900", "29161", "41328", "56953", "76636", "101025", "130816", "166753", "209628", "260281", "319600", "388521", "468028", "559153", "662976", "780625", "913276", "1062153", "1228528", "1413721", "1619100", "1846081" ]
[ "nonn", "nice", "easy" ]
158
0
5
[ "A000290", "A000384", "A000447", "A000583", "A002309", "A002593", "A253724", "A253725", "A260810" ]
[ "M5199", "N2262" ]
N. J. A. Sloane
2024-04-19T12:06:01
oeisdata/seq/A002/A002593.seq
e163a3b7d939ff873604971e9e658933
A002594
a(n) = n^2*(16*n^4-20*n^2+7)/3.
[ "1", "244", "3369", "20176", "79225", "240276", "611569", "1370944", "2790801", "5266900", "9351001", "15787344", "25552969", "39901876", "60413025", "89042176", "128177569", "180699444", "250043401", "340267600", "456123801", "603132244", "787660369", "1017005376", "1299480625", "1644505876", "2062701369", "2565985744", "3167677801", "3882602100", "4727198401", "5719634944", "6879925569", "8230050676" ]
[ "nonn", "easy" ]
43
0
5
[ "A000539", "A002594", "A016757" ]
[ "M5421", "N2354" ]
N. J. A. Sloane. The old definition was wrong - entry revised by N. J. A. Sloane, Jun 10 2012. It is possible that the Croxton and Crowden reference gives a better explanation than the simple formula in the new definition.
2022-09-08T08:44:31
oeisdata/seq/A002/A002594.seq
d95292787df42e8a695c2a80d149ec0e
A002595
Denominators of Taylor series expansion of arcsin(x). Also arises from arccos(x), arccsc(x), arcsec(x), arcsinh(x).
[ "1", "6", "40", "112", "1152", "2816", "13312", "10240", "557056", "1245184", "5505024", "12058624", "104857600", "226492416", "973078528", "2080374784", "23622320128", "30064771072", "635655159808", "446676598784", "11269994184704", "23639499997184", "6597069766656" ]
[ "nonn", "frac", "nice", "easy" ]
47
0
5
[ "A000165", "A001147", "A002595", "A055786", "A143582", "A162443", "G1" ]
[ "M4233", "N1768" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002595.seq
b3d21f48d18ad7a33f2158a8ffecea43
A002596
Numerators in expansion of sqrt(1+x). Absolute values give numerators in expansion of sqrt(1-x).
[ "1", "1", "-1", "1", "-5", "7", "-21", "33", "-429", "715", "-2431", "4199", "-29393", "52003", "-185725", "334305", "-9694845", "17678835", "-64822395", "119409675", "-883631595", "1641030105", "-6116566755", "11435320455", "-171529806825", "322476036831", "-1215486600363", "2295919134019" ]
[ "easy", "nice", "frac", "sign" ]
97
0
5
[ "A000108", "A000265", "A001795", "A001803", "A002596", "A046161", "A098597", "A161198", "A161200", "A161202" ]
[ "M3768", "N1538" ]
N. J. A. Sloane
2025-02-16T08:32:26
oeisdata/seq/A002/A002596.seq
d9d6ddd57f9586413ae0e172a9b87649
A002597
Number of partitions into one kind of 1's, two kinds of 2's, and three kinds of 3's.
[ "1", "1", "3", "6", "9", "15", "25", "34", "51", "73", "97", "132", "178", "226", "294", "376", "466", "582", "722", "872", "1062", "1282", "1522", "1812", "2147", "2507", "2937", "3422", "3947", "4557", "5243", "5978", "6825", "7763", "8771", "9912", "11172", "12516", "14028", "15680", "17444", "19404", "21540", "23808", "26316", "29028", "31908" ]
[ "nonn" ]
44
0
5
[ "A002597", "A064349" ]
[ "M2533", "N1000" ]
N. J. A. Sloane
2023-06-25T15:52:42
oeisdata/seq/A002/A002597.seq
1f738f9c0c7a52262532ef5a467ab080
A002598
A generalized partition function.
[ "1", "6", "9", "13", "19", "37", "58", "97", "143", "227", "328", "492", "688", "992", "1364", "1903", "2551", "3473", "4586", "6097", "7911", "10333", "13226", "16988", "21454", "27172", "33938", "42437", "52423", "64833", "79354", "97130", "117824", "142930", "172018", "206925", "247179", "295105", "350154", "415124", "489414", "576540" ]
[ "nonn", "easy" ]
30
0
5
[ "A002598", "A064349" ]
[ "M4077", "N1693" ]
N. J. A. Sloane
2023-10-17T06:11:55
oeisdata/seq/A002/A002598.seq
ea364c67cf9136673d9080675a8948d1
A002599
A generalized partition function.
[ "1", "6", "15", "19", "24", "42", "73", "127", "208", "337", "528", "827", "1263", "1902", "2819", "4133", "5986", "8578", "12146", "17057", "23711", "32708", "44726", "60713", "81800", "109468", "145526", "192288", "252521", "329792", "428316", "553478", "711596", "910563", "1159790", "1470798", "1857286", "2335838" ]
[ "nonn" ]
28
0
5
null
[ "M4106", "N1703" ]
N. J. A. Sloane
2023-10-17T07:41:20
oeisdata/seq/A002/A002599.seq
4565efb1f4a83b7396b23335b45e1f25
A002600
A generalized partition function.
[ "1", "10", "25", "37", "42", "48", "79", "145", "244", "415", "672", "1100", "1722", "2727", "4193", "6428", "9658", "14478", "21313", "31304", "45329", "65311", "93074", "132026", "185413", "259242", "359395", "495839", "679175", "926064", "1254360", "1691753", "2268267", "3028345", "4021954", "5320139", "7003154" ]
[ "nonn" ]
27
0
5
null
[ "M4686", "N2002" ]
N. J. A. Sloane
2023-10-17T08:18:51
oeisdata/seq/A002/A002600.seq
451e7169981d5f22a10c3dfdbe86c90a