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christopher
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oeis

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2
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stringlengths
7
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1
348
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1
8
score
int64
1
2.35k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
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cross_references
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1
128
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231
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-07-19 00:40:46
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A356601
Triangle read by rows. T(n, k) = denominator(Integral_{z=0..1} Eulerian(n, k)*z^(k + 1)*(z - 1)^(n - k - 1) dz), where Eulerian(n, k) = A173018(n, k), for n >= 1, and T(0, 0) = 1.
[ "1", "2", "1", "6", "3", "1", "12", "3", "4", "1", "20", "30", "20", "5", "1", "30", "30", "10", "15", "6", "1", "42", "35", "70", "105", "14", "7", "1", "56", "7", "280", "35", "56", "7", "8", "1", "72", "252", "56", "630", "504", "28", "72", "9", "1", "90", "180", "105", "630", "126", "420", "45", "45", "10", "1", "110", "495", "33", "1155", "1386", "1155", "165", "99", "110", "11", "1" ]
[ "nonn", "tabl", "frac" ]
19
0
2
[ "A173018", "A278075", "A356545", "A356547", "A356601", "A356602" ]
null
Peter Luschny, Aug 15 2022
2023-12-10T11:10:48
oeisdata/seq/A356/A356601.seq
5685426158fb7874277182193afb0f7d
A356602
Triangle read by rows. T(n, k) = numerator(Integral_{z=0..1} Eulerian(n, k)*z^(k + 1)*(z - 1)^(n - k - 1) dz), where Eulerian(n, k) = A173018(n, k) for n >= 1, and T(0, 0) = 1.
[ "1", "1", "0", "-1", "1", "0", "1", "-1", "1", "0", "-1", "11", "-11", "1", "0", "1", "-13", "11", "-13", "1", "0", "-1", "19", "-151", "302", "-19", "1", "0", "1", "-5", "1191", "-302", "397", "-15", "1", "0", "-1", "247", "-477", "15619", "-15619", "477", "-247", "1", "0", "1", "-251", "1826", "-44117", "15619", "-44117", "1826", "-251", "1", "0" ]
[ "sign", "tabl", "frac" ]
15
0
12
[ "A173018", "A278075", "A356545", "A356547", "A356601", "A356602" ]
null
Peter Luschny, Aug 15 2022
2023-12-10T11:10:43
oeisdata/seq/A356/A356602.seq
462136f0db1df25dd9ec4dfe637cefc5
A356603
Position in A356226 of first appearance of the n-th composition in standard order (row n of A066099).
[ "1", "2", "4", "10", "8", "20", "50", "110", "16", "40", "100", "220", "250", "550", "1210", "1870", "32", "80", "200", "440", "500", "1100", "2420", "3740", "1250", "2750", "6050", "9350", "13310", "20570", "31790", "43010", "64", "160", "400", "880", "1000", "2200", "4840", "7480", "2500", "5500", "12100", "18700", "26620", "41140", "63580", "86020" ]
[ "nonn" ]
7
0
2
[ "A000005", "A001221", "A001222", "A001414", "A053251", "A055932", "A061395", "A066205", "A066208", "A073491", "A073492", "A073493", "A132747", "A137921", "A193829", "A286470", "A287170", "A356224", "A356226", "A356227", "A356228", "A356229", "A356230", "A356231", "A356232", "A356237", "A356603", "A356604" ]
null
Gus Wiseman, Aug 30 2022
2022-08-30T09:41:41
oeisdata/seq/A356/A356603.seq
6f23cd773d08e54b4f85a6fdb8a62032
A356604
Number of integer compositions of n into odd parts covering an initial interval of odd positive integers.
[ "1", "1", "1", "1", "3", "4", "5", "9", "13", "24", "40", "61", "101", "160", "257", "415", "679", "1103", "1774", "2884", "4656", "7517", "12165", "19653", "31753", "51390", "83134", "134412", "217505", "351814", "569081", "920769", "1489587", "2409992", "3899347", "6309059", "10208628", "16518910", "26729830", "43254212", "69994082" ]
[ "nonn" ]
10
0
5
[ "A000009", "A000041", "A000045", "A001221", "A001222", "A001227", "A005408", "A011782", "A053251", "A055932", "A060142", "A061395", "A066205", "A066208", "A073493", "A107428", "A107429", "A137921", "A324969", "A333217", "A356224", "A356232", "A356603", "A356604", "A356605" ]
null
Gus Wiseman, Aug 30 2022
2022-09-01T19:48:14
oeisdata/seq/A356/A356604.seq
ae594c1b4d453b07a8c4708fe530d95c
A356605
Number of integer compositions of n into odd parts covering an interval of odd positive integers.
[ "1", "1", "1", "2", "3", "5", "6", "10", "15", "26", "41", "65", "104", "164", "262", "424", "687", "1112", "1792", "2898", "4677", "7556", "12197", "19699", "31836", "51466", "83234", "134593", "217674", "352057", "569452", "921165", "1490173", "2410784", "3900288", "6310436", "10210358", "16521108", "26733020", "43258086", "69999295" ]
[ "nonn" ]
13
0
4
[ "A000009", "A000041", "A000045", "A001227", "A011782", "A053251", "A055932", "A060142", "A066205", "A066208", "A073491", "A107428", "A107429", "A137921", "A324969", "A332032", "A333217", "A356224", "A356232", "A356604", "A356605", "A356737", "A356841", "A356846" ]
null
Gus Wiseman, Aug 31 2022
2022-09-01T19:48:07
oeisdata/seq/A356/A356605.seq
d69cb80c29596673b562a2a11761c906
A356606
Number of strict integer partitions of n where all parts have neighbors.
[ "1", "0", "0", "1", "0", "1", "1", "1", "0", "2", "1", "1", "2", "1", "2", "3", "2", "2", "5", "2", "4", "5", "5", "4", "8", "5", "7", "9", "8", "8", "13", "10", "11", "16", "13", "15", "20", "18", "18", "27", "21", "26", "31", "30", "30", "43", "34", "42", "49", "48", "48", "65", "56", "65", "76", "74", "77", "97", "88", "98", "117", "111", "119", "143", "137", "146", "175", "165", "182", "208" ]
[ "nonn" ]
25
0
10
[ "A000009", "A000041", "A000837", "A007690", "A137921", "A183558", "A289509", "A325160", "A328171", "A328172", "A328187", "A328220", "A328221", "A355393", "A355394", "A356235", "A356236", "A356237", "A356606", "A356607" ]
null
Gus Wiseman, Aug 24 2022
2024-02-24T10:05:21
oeisdata/seq/A356/A356606.seq
e7dfdf9faf8962d16bc4715ec47f4542
A356607
Number of strict integer partitions of n with at least one neighborless part.
[ "0", "1", "1", "1", "2", "2", "3", "4", "6", "6", "9", "11", "13", "17", "20", "24", "30", "36", "41", "52", "60", "71", "84", "100", "114", "137", "158", "183", "214", "248", "283", "330", "379", "432", "499", "570", "648", "742", "846", "955", "1092", "1234", "1395", "1580", "1786", "2005", "2270", "2548", "2861", "3216", "3610", "4032", "4526", "5055", "5642", "6304", "7031", "7820", "8720", "9694" ]
[ "nonn" ]
20
0
5
[ "A000009", "A000041", "A000837", "A007690", "A073492", "A137921", "A183558", "A289509", "A325160", "A328171", "A328172", "A328187", "A328220", "A328221", "A355393", "A355394", "A356235", "A356236", "A356606", "A356607" ]
null
Gus Wiseman, Aug 26 2022
2024-02-12T16:32:02
oeisdata/seq/A356/A356607.seq
a6b27bf08db61a0368ed9f55e5a1f471
A356608
a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(24^k * (n - 4*k)!).
[ "1", "1", "1", "1", "1", "6", "31", "106", "281", "1261", "13861", "106261", "558361", "2709136", "32802771", "447762316", "4093711441", "28011714641", "293624974441", "5549250905281", "80454378591121", "815886496908946", "8379058314620071", "168672787637953446", "3514729162490432041", "51656083670790267901" ]
[ "nonn" ]
26
0
6
[ "A354436", "A354552", "A356029", "A356328", "A356608", "A356630", "A356634" ]
null
Seiichi Manyama, Aug 18 2022
2022-09-14T09:34:30
oeisdata/seq/A356/A356608.seq
bb811ea09d5c1eb2cb54fb36013b448f
A356609
Numbers k that can be written as the sum of 6 divisors of k (not necessarily distinct).
[ "6", "8", "10", "12", "14", "16", "18", "20", "24", "28", "30", "32", "36", "40", "42", "44", "48", "50", "52", "54", "56", "60", "64", "66", "70", "72", "78", "80", "84", "88", "90", "96", "98", "100", "102", "104", "108", "110", "112", "114", "120", "126", "128", "130", "132", "136", "138", "140", "144", "150", "152", "154", "156", "160", "162", "168", "170", "174", "176", "180", "182", "184", "186", "190" ]
[ "nonn" ]
30
1
1
[ "A000027", "A299174", "A354591", "A355200", "A355641", "A356609", "A356635", "A356657", "A356659", "A356660" ]
null
Wesley Ivan Hurt, Aug 18 2022
2023-08-08T03:22:18
oeisdata/seq/A356/A356609.seq
fb5fde3c09593728259bd20dcf8bdb27
A356610
Number of SAWs crossing a rhomboidal domain of the hexagonal lattice.
[ "2", "14", "316", "25092", "7374480", "8029311942", "32223151155864", "476605408516689238", "26016526700583361056456", "5246595079903462547245876694", "3911053741699230141571030313824664", "10780907768757190963361134040036893772360", "109919900687141309301630828947780890728732496678" ]
[ "nonn" ]
6
1
1
[ "A001006", "A002026", "A007764", "A116485", "A356610" ]
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:16:20
oeisdata/seq/A356/A356610.seq
7274bd6a68feb382c0a07b12d15a9b96
A356611
Number of SAWs spanning a rhomboidal domain of the hexagonal lattice.
[ "2", "50", "2256", "292006", "124394172", "182189852062", "937116505296162", "17167376550995687961", "1130911800993488803731078", "269650395624478266477331223678", "233772496350603982679550385266064014", "739330863241806743025423160490836132227125", "8551000409049037000098287028025432585191736309022" ]
[ "nonn" ]
6
1
1
[ "A001006", "A002026", "A007764", "A116485", "A356611" ]
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:16:04
oeisdata/seq/A356/A356611.seq
99c0e3ef0dcdd1fd00a2e94e5e27ae5c
A356612
Number of SAPs crossing a rhomboidal domain of the hexagonal lattice.
[ "1", "3", "48", "3126", "775842", "727870836", "2575728525240", "34244061451559094", "1703999058661009145746", "316543880488539946466963896", "219157996022284922702859434801868", "564858713948847373563461482383973674774", "5415142061627863782256892670635702203299498106" ]
[ "nonn" ]
6
1
2
[ "A001006", "A002026", "A007764", "A116485", "A356612" ]
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:15:49
oeisdata/seq/A356/A356612.seq
7a2ea25b3e912ccc306a8f9546e9a31d
A356613
Number of SAWs crossing a triangular domain of the hexagonal lattice.
[ "2", "7", "44", "515", "11500", "493704", "40751496", "6463642330", "1970190022696", "1154437344815284", "1300686960810345198", "2818300749120970598426", "11745284697899678209887246", "94153940687296424300453605522", "1451915619132744566900848537333082", "43072062058620235613855525243039798546" ]
[ "nonn" ]
6
1
1
[ "A001006", "A002026", "A007764", "A116485", "A356613" ]
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:15:36
oeisdata/seq/A356/A356613.seq
3d39be2c76689f143e3f34d76036779f
A356614
Number of SAWs crossing a triangular domain of the hexagonal lattice and including the top vertex.
[ "1", "3", "18", "210", "4716", "203130", "16781528", "2661898722", "811337884328", "475395297020430", "535618774376758222", "1160567857061063474508", "4836675324919658534327348", "38772333263059858336182467950", "597894854584620490267288203881970", "17736956492510173648327596231133813426" ]
[ "nonn" ]
6
1
2
[ "A001006", "A002026", "A007764", "A116485", "A356614" ]
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:15:25
oeisdata/seq/A356/A356614.seq
41accd18f26792b550d508dadce2bb85
A356615
Number of SAPs crossing a triangular domain of the hexagonal lattice.
[ "1", "2", "9", "85", "1605", "59896", "4392639", "629739138", "175745776816", "95207239875508", "99934927799315359", "202993550188918062298", "797200289814680588454420", "6048794511036987586252009778", "88623124229469033988344357343229", "2506168305598107863294101582119745559" ]
[ "nonn" ]
6
1
2
[ "A001006", "A002026", "A007764", "A116485", "A356615" ]
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:15:11
oeisdata/seq/A356/A356615.seq
da7c45bd2005a0004a2e8fcd05743642
A356616
Number of SAPs crossing a triangular domain of the hexagonal lattice and including top vertex.
[ "1", "1", "4", "36", "666", "24696", "1808820", "259300148", "72369408510", "39205936157880", "41152969216872016", "83592236529606631688", "328284931491454739745904", "2490876950205850778116435156", "36494758452603010620499864088198", "1032033208911845667821292289616451218" ]
[ "nonn" ]
6
1
3
[ "A001006", "A002026", "A007764", "A116485", "A356616" ]
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:14:52
oeisdata/seq/A356/A356616.seq
caee1e26fbb181b2ecbde15d08fa8e47
A356617
Number of square lattice worms w_n.
[ "1", "1", "3", "7", "19", "41", "113", "261", "713", "1681", "4567", "10993", "29717", "72493", "195269", "481261", "1292729", "3211263", "8606801", "21515135", "57561815", "144631085", "386382359", "974968645", "2601469419", "6587913395", "17560287513", "44605607915", "118794020215", "302552020141", "805154546027" ]
[ "nonn" ]
6
1
3
null
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:13:51
oeisdata/seq/A356/A356617.seq
95e43ec6718910cf9dce42cb074c8554
A356618
Number of triangular lattice worms w_n.
[ "1", "3", "11", "41", "155", "603", "2361", "9321", "37015", "147657", "591227", "2374539", "9561487", "38585555", "156007667", "631806555", "2562434223", "10405918209", "42306525037", "172180092143", "701397054549", "2859651782649", "11668050956347", "47642140547239", "194655761552949", "795800965884627" ]
[ "nonn" ]
6
1
2
null
null
Vaclav Kotesovec, following a suggestion from Anthony Guttmann, Aug 16 2022
2022-08-16T05:13:33
oeisdata/seq/A356/A356618.seq
52cad1ed7b39acc7162cedaa8fec4dd7
A356619
a(n) = number of k-tuples (u(1), u(2), ..., u(k)) with 1 <= u(1) < u(2) < ... < u(k) <= n such that u(i) - u(i-1) <= 3 for i = 2,...,k.
[ "0", "1", "4", "11", "25", "52", "103", "198", "374", "699", "1298", "2401", "4431", "8166", "15037", "27676", "50924", "93685", "172336", "316999", "583077", "1072472", "1972611", "3628226", "6673378", "12274287", "22575966", "41523709", "76374043", "140473802", "258371641", "475219576", "874065112", "1607656425" ]
[ "nonn", "easy" ]
23
0
3
[ "A001891", "A062544", "A221949", "A356619", "A356620", "A356621" ]
null
Clark Kimberling, Aug 24 2022
2022-09-04T12:55:57
oeisdata/seq/A356/A356619.seq
eeab5bf2cb8dbe3de55ae1d4c0beb141
A356620
a(n) = number of k-tuples (u(1), u(2), ..., u(k)) with 1 <= u(1) < u(2) < ... < u(k) <= n such that u(i) - u(i-1) <= 4 for i = 2,...,k.
[ "0", "1", "4", "11", "26", "56", "115", "230", "453", "884", "1716", "3321", "6416", "12383", "23886", "46060", "88803", "171194", "330009", "636136", "1226216", "2363633", "4556076", "8782147", "16928162", "32630112", "62896595", "121237118", "233692093", "450456028", "868281948", "1673667305", "3226097496", "6218502903" ]
[ "nonn", "easy" ]
12
0
3
[ "A001891", "A356619", "A356620", "A356621" ]
null
Clark Kimberling, Sep 04 2022
2022-09-07T12:27:18
oeisdata/seq/A356/A356620.seq
ded29fed9abf3f157907eaab0775350b
A356621
a(n) = number of k-tuples (u(1), u(2), ..., u(k)) with 1 <= u(1) < u(2) < ... < u(k) <= n such that u(i) - u(i-1) <= 5 for i = 2,...,k.
[ "0", "1", "4", "11", "26", "57", "119", "242", "485", "964", "1907", "3762", "7410", "14583", "28686", "56413", "110924", "218091", "428777", "842976", "1657271", "3258134", "6405349", "12592612", "24756452", "48669933", "95682600", "188107071", "369808798", "727024989", "1429293531", "2809917134", "5524151673" ]
[ "nonn", "easy" ]
14
0
3
[ "A001891", "A356619", "A356620", "A356621" ]
null
Clark Kimberling, Sep 04 2022
2022-09-30T09:41:52
oeisdata/seq/A356/A356621.seq
78eaa63da5ca2f78dce24520485916f7
A356622
Number of ways to tile a hexagonal strip made up of 4*n equilateral triangles, using triangles and diamonds.
[ "1", "5", "39", "317", "2585", "21085", "171987", "1402873", "11443033", "93339173", "761354199", "6210256613", "50656169297", "413195081581", "3370372805763", "27491645850097", "224245398092113", "1829137434684101", "14920010771362215" ]
[ "nonn", "easy" ]
11
0
2
[ "A355327", "A356622", "A356623" ]
null
Greg Dresden and Aarnav Gogri, Aug 16 2022
2022-08-17T22:39:50
oeisdata/seq/A356/A356622.seq
34440697ff21e5897b3e412bc7e91692
A356623
Number of ways to tile a hexagonal strip made up of 4*n+2 equilateral triangles, using triangles and diamonds.
[ "2", "18", "148", "1208", "9854", "80378", "655632", "5347896", "43622018", "355818522", "2902360468", "23674136576", "193106524430", "1575142124306", "12848207584320", "104800979913168", "854846508252578", "6972859922465346", "56876614724333236" ]
[ "nonn" ]
26
0
1
[ "A190984", "A356622", "A356623" ]
null
Greg Dresden and Aarnav Gogri, Aug 17 2022
2023-07-04T14:24:33
oeisdata/seq/A356/A356623.seq
e668de117acd252d91917d1371ed5e92
A356624
After n iterations of the "Square Multiscale" substitution, the largest tiles have side length 3^t / 5^f; a(n) = t (A356625 gives corresponding f's).
[ "0", "1", "2", "3", "0", "4", "1", "5", "2", "6", "3", "0", "7", "4", "1", "8", "5", "2", "9", "6", "3", "0", "10", "7", "4", "1", "11", "8", "5", "2", "12", "9", "6", "3", "0", "13", "10", "7", "4", "1", "14", "11", "8", "5", "2", "15", "12", "9", "6", "3", "0", "16", "13", "10", "7", "4", "1", "17", "14", "11", "8", "5", "2", "18", "15", "12", "9", "6", "3", "0", "19", "16", "13", "10", "7", "4", "1", "20", "17" ]
[ "nonn" ]
14
0
3
[ "A022336", "A329919", "A354535", "A356624", "A356625" ]
null
Rémy Sigrist, Aug 17 2022
2022-08-21T06:15:11
oeisdata/seq/A356/A356624.seq
364eb3d4e9cbb647275906c2d39edb40
A356625
After n iterations of the "Square Multiscale" substitution, the largest tiles have side length 3^t / 5^f; a(n) = f (A356624 gives corresponding t's).
[ "0", "1", "2", "3", "1", "4", "2", "5", "3", "6", "4", "2", "7", "5", "3", "8", "6", "4", "9", "7", "5", "3", "10", "8", "6", "4", "11", "9", "7", "5", "12", "10", "8", "6", "4", "13", "11", "9", "7", "5", "14", "12", "10", "8", "6", "15", "13", "11", "9", "7", "5", "16", "14", "12", "10", "8", "6", "17", "15", "13", "11", "9", "7", "18", "16", "14", "12", "10", "8", "6", "19", "17", "15", "13", "11", "9", "7" ]
[ "nonn" ]
13
0
3
[ "A022337", "A329919", "A354535", "A356624", "A356625" ]
null
Rémy Sigrist, Aug 17 2022
2022-08-21T06:15:28
oeisdata/seq/A356/A356625.seq
74cd507e69faedf129dc15ee000cb730
A356626
Position of A332979(n) in the Doudna sequence A005940.
[ "1", "2", "4", "7", "15", "29", "61", "125", "249", "497", "1009", "2033", "4081", "8177", "16369", "32753", "65521", "131057", "262081", "524225", "1048513", "2097089", "4194241", "8388545", "16777153", "33553921", "67108353", "134217217", "268434945", "536870401", "1073741313", "2147483137", "4294966785", "8589934081", "17179868673" ]
[ "nonn" ]
9
0
2
[ "A000120", "A000961", "A005940", "A006530", "A023416", "A023758", "A180944", "A332979", "A356626" ]
null
Michael De Vlieger, Aug 24 2022
2022-09-08T01:35:05
oeisdata/seq/A356/A356626.seq
8b0cb002b22b046de0b4ce797b0c0328
A356627
Primes whose powers appear in A332979.
[ "2", "3", "5", "7", "11", "17", "29", "37", "41", "59", "67", "71", "97", "127", "149", "191", "223", "269", "307", "347", "419", "431", "557", "563", "569", "587", "593", "599", "641", "727", "809", "937", "967", "1009", "1213", "1277", "1423", "1861", "1973", "2237", "2267", "2657", "3163", "3299", "3449", "3457", "3527", "3907", "4001", "4211", "4441", "4637" ]
[ "nonn" ]
10
1
1
[ "A000040", "A000961", "A005940", "A180944", "A180945", "A302334", "A332979", "A356627" ]
null
Michael De Vlieger, Sep 27 2022
2022-09-30T23:09:53
oeisdata/seq/A356/A356627.seq
602e3371b0b3a657c692840386ea332a
A356628
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(n - 2*k)!.
[ "1", "1", "1", "7", "25", "181", "1561", "12811", "188497", "2071945", "38889361", "620762671", "12917838121", "291278938237", "6667342764265", "194869722610291", "5137978752994081", "177509783765281681", "5610285632192738977", "215195998789004395735", "8228064506323330305721" ]
[ "nonn" ]
20
0
4
[ "A216688", "A354436", "A356628", "A356629", "A356630", "A356632", "A358064" ]
null
Seiichi Manyama, Aug 18 2022
2022-11-01T11:55:53
oeisdata/seq/A356/A356628.seq
5bdee9a4b10a9414a0b43f1030e4a445
A356629
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(n - 3*k)!.
[ "1", "1", "1", "1", "25", "121", "361", "5881", "82321", "547345", "6053041", "167991121", "2179469161", "22892967241", "788375451865", "18046198202761", "245523704069281", "7548055281543841", "270833271588545761", "5369819950838359585", "141456920470310708281", "6760255576117937586841" ]
[ "nonn" ]
21
0
5
[ "A354436", "A354553", "A356628", "A356629", "A356630", "A356633", "A358065" ]
null
Seiichi Manyama, Aug 18 2022
2022-11-01T12:10:35
oeisdata/seq/A356/A356629.seq
e910cedfa5c8e262ace17554ec9aade4
A356630
a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(n - 4*k)!.
[ "1", "1", "1", "1", "1", "121", "721", "2521", "6721", "378001", "7287841", "59930641", "319429441", "7524471241", "353072319601", "5897248517161", "55827317669761", "726274560953761", "53139878190826561", "1650487849152976801", "25981849479032542081", "317292238756098973081" ]
[ "nonn" ]
14
0
6
[ "A354436", "A354554", "A356628", "A356629", "A356630", "A356634" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-19T09:25:16
oeisdata/seq/A356/A356630.seq
e96ce2b31b0a7afccf3c9d6b51d58d0d
A356631
a(n) is the least number k such that the sum (with multiplicity) of prime factors of k*(k+1)*...*(k+n-1) is a perfect power.
[ "1", "4", "2", "1", "4", "5", "2", "1", "11", "18", "8", "12", "8", "15", "4", "41", "10", "65", "10", "39", "21", "5", "54", "30", "25", "2", "1", "17", "43", "2", "1", "80", "12", "41", "206", "11", "70", "39", "81", "5", "289", "50", "18", "56", "24", "10", "49", "103", "146", "77", "53", "582", "31", "58", "37", "419", "140", "174", "77", "44", "100", "168", "44", "42", "99", "13", "11", "80", "60", "101", "71", "12", "24", "70", "11", "52", "671" ]
[ "nonn" ]
12
1
2
[ "A001414", "A001597", "A356631", "A356646" ]
null
J. M. Bergot and Robert Israel, Aug 18 2022
2022-09-05T09:10:32
oeisdata/seq/A356/A356631.seq
ab4f49b27c0e3957291e663a6d2b1b3f
A356632
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/2^k.
[ "1", "1", "2", "9", "48", "330", "2880", "29610", "362880", "5148360", "83462400", "1535549400", "31614105600", "724183059600", "18307441152000", "507367438578000", "15336404987904000", "502812808754256000", "17805001275629568000", "678167395781763888000", "27681559049033809920000" ]
[ "nonn" ]
13
0
3
[ "A352944", "A356632", "A356633", "A356634" ]
null
Seiichi Manyama, Aug 18 2022
2022-11-01T11:24:55
oeisdata/seq/A356/A356632.seq
1647ee993b8b702017d71df5edf572e3
A356633
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/6^k.
[ "1", "1", "2", "6", "28", "160", "1080", "8540", "78400", "816480", "9492000", "122337600", "1736380800", "26930904000", "453515462400", "8254694448000", "161734564992000", "3397235761920000", "76228261933824000", "1821644243362944000", "46233794313907200000", "1242946827521118720000" ]
[ "nonn" ]
11
0
3
[ "A352946", "A356632", "A356633", "A356634" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-19T09:25:51
oeisdata/seq/A356/A356633.seq
d5cc966183ca9c37a7be8aa7faac6abe
A356634
a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/24^k.
[ "1", "1", "2", "6", "24", "125", "780", "5670", "47040", "439110", "4561200", "52182900", "651974400", "8832874050", "129001672800", "2020822303500", "33805804032000", "601587281295000", "11348960759136000", "226275153994890000", "4755046903326720000", "105061084389756495000", "2435176811445618240000" ]
[ "nonn" ]
11
0
3
[ "A356632", "A356633", "A356634" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-19T09:25:56
oeisdata/seq/A356/A356634.seq
e4deaaffd896cd3df7257b4f7d1e2a34
A356635
Numbers k that can be written as the sum of 7 divisors of k (not necessarily distinct).
[ "7", "8", "9", "10", "12", "14", "15", "16", "18", "20", "21", "22", "24", "27", "28", "30", "32", "33", "35", "36", "39", "40", "42", "44", "45", "48", "49", "50", "52", "54", "55", "56", "60", "63", "64", "66", "68", "70", "72", "75", "77", "78", "80", "81", "84", "88", "90", "91", "96", "98", "99", "100", "102", "104", "105", "108", "110", "112", "114", "117", "119", "120", "126", "128", "130" ]
[ "nonn" ]
22
1
1
[ "A000027", "A299174", "A354591", "A355200", "A355641", "A356609", "A356635", "A356657", "A356659", "A356660" ]
null
Wesley Ivan Hurt, Aug 18 2022
2023-08-08T03:22:21
oeisdata/seq/A356/A356635.seq
07a9ab9382b9a298a3c1e1545450e418
A356636
Triangle read by rows. T(n, k) = binomial(n, k) * n!^2 / floor(n/2)!^2.
[ "1", "1", "1", "4", "8", "4", "36", "108", "108", "36", "144", "576", "864", "576", "144", "3600", "18000", "36000", "36000", "18000", "3600", "14400", "86400", "216000", "288000", "216000", "86400", "14400", "705600", "4939200", "14817600", "24696000", "24696000", "14817600", "4939200", "705600" ]
[ "nonn", "tabl" ]
6
0
4
[ "A056040", "A193282", "A253666", "A356636" ]
null
Peter Luschny, Aug 19 2022
2022-08-19T02:48:25
oeisdata/seq/A356/A356636.seq
2617eecf7375a6bfd97acac407a4c28e
A356637
a(n) = A000265(A263931(n)).
[ "1", "1", "1", "1", "1", "9", "3", "3", "45", "5", "1", "21", "7", "175", "675", "45", "45", "1485", "5775", "5775", "45045", "2145", "195", "8775", "2925", "5733", "22491", "833", "6545", "373065", "24871", "24871", "1566873", "3086265", "181545", "357903", "39767", "39767", "156975", "309925", "61985", "5020785", "239085", "20322225", "160730325" ]
[ "nonn" ]
29
0
6
[ "A000265", "A000984", "A001316", "A006519", "A056040", "A059097", "A261130", "A263931", "A356637" ]
null
Peter Luschny, Sep 07 2022
2022-09-08T05:47:33
oeisdata/seq/A356/A356637.seq
71f1588a16583f648d23c6802abe34f2
A356638
Odd composite numbers k such that 2^((k-1)/2) == -1 (mod k).
[ "3277", "29341", "49141", "80581", "88357", "104653", "196093", "314821", "458989", "476971", "489997", "800605", "838861", "873181", "877099", "1004653", "1251949", "1302451", "1325843", "1373653", "1397419", "1441091", "1507963", "1509709", "1530787", "1678541", "1811573", "1907851", "1987021", "2004403", "2269093" ]
[ "nonn" ]
7
1
1
[ "A244626", "A244628", "A356638" ]
null
Jeppe Stig Nielsen, Aug 19 2022
2022-08-19T09:13:46
oeisdata/seq/A356/A356638.seq
10402fb97bd88505c402bf07ae6d052c
A356639
Number of integer sequences b with b(1) = 1, b(m) > 0 and b(m+1) - b(m) > 0, of length n which transform under the map S into a nonnegative integer sequence. The transform c = S(b) is defined by c(m) = Product_{k=1..m} b(k) / Product_{k=2..m} (b(k) - b(k-1)).
[ "1", "1", "3", "17", "155", "2677", "73327", "3578339", "329652351" ]
[ "more", "nonn" ]
51
1
3
[ "A000005", "A000027", "A000045", "A000079", "A000142", "A001405", "A001654", "A004277", "A006501", "A008233", "A010551", "A019442", "A019464", "A026549", "A031923", "A038754", "A057895", "A058295", "A062112", "A066332", "A079352", "A082458", "A087811", "A093968", "A098011", "A098558", "A100071", "A100538", "A111286", "A137326", "A138278", "A166447", "A171647", "A205825", "A208147", "A264557", "A264635", "A308546", "A329227", "A336496", "A349079", "A349080", "A356639", "A359039" ]
null
Thomas Scheuerle, Aug 19 2022
2024-08-01T09:19:00
oeisdata/seq/A356/A356639.seq
45e1808a2559392eea2b8940ca4e0d0c
A356640
a(n) is the least number k such that the least base in which k is a Niven number is n, i.e., A356552(k) = n, or -1 if no such k exists.
[ "1", "3", "50", "5", "44", "7", "161", "119", "201", "11", "253", "13", "494", "226", "1444", "17", "799", "19", "437", "1189", "957", "23", "1081", "2263", "755", "767", "927", "29", "932", "31", "1147", "5141", "1191", "1226", "2009", "37", "1517", "1522", "1641", "41", "1927", "43", "2021", "2026", "2164", "47", "2491", "4559", "5001", "2602", "2757", "53", "2972" ]
[ "nonn", "base" ]
12
2
2
[ "A005349", "A049445", "A064150", "A064438", "A064481", "A249634", "A356552", "A356640" ]
null
Amiram Eldar, Aug 19 2022
2022-08-23T10:50:20
oeisdata/seq/A356/A356640.seq
efce4fa32e5bb2abc752eedcfae33760
A356641
Indices of records in A356640.
[ "2", "3", "4", "8", "10", "12", "14", "16", "25", "33", "56", "63", "64", "75", "78", "81", "93", "120", "121", "125", "144", "160", "162", "169", "172", "196", "216", "225", "237", "244", "256", "288", "320", "361", "400", "456", "474", "484", "513", "592", "634", "676", "784", "808", "961", "1089", "1369", "1936", "2286", "2302", "2360", "2362", "2397", "2401" ]
[ "nonn", "base" ]
8
1
1
[ "A356552", "A356640", "A356641", "A356642" ]
null
Amiram Eldar, Aug 19 2022
2022-09-07T15:45:41
oeisdata/seq/A356/A356641.seq
c3963a5b9743623459b0983e0e9aa47d
A356642
Record values in A356640.
[ "1", "3", "50", "161", "201", "253", "494", "1444", "2263", "5141", "5695", "8153", "9271", "10877", "18337", "23377", "23989", "30353", "33017", "50003", "51947", "55067", "55867", "56279", "88922", "94231", "95251", "100127", "131021", "134899", "169141", "252566", "314563", "323729", "389113", "415883", "453613", "523147", "902219", "1017505" ]
[ "nonn", "base" ]
5
1
2
[ "A356552", "A356640", "A356641", "A356642" ]
null
Amiram Eldar, Aug 19 2022
2022-08-23T09:51:16
oeisdata/seq/A356/A356642.seq
549e59155ccd1c37373f0ed2c031eb7b
A356643
a(n) is the number of order-n magic triangles composed of the numbers from 1 to n(n+1)/2 in which the sum of the k-th row and the (n-k)-th row is same for all k and all three directions, counted up to rotations and reflections.
[ "1", "0", "0", "0", "612", "22411", "0" ]
[ "nonn", "more" ]
14
1
5
[ "A000217", "A004767", "A006052", "A342467", "A355119", "A356643" ]
null
Donghwi Park, Aug 19 2022
2022-10-05T05:00:24
oeisdata/seq/A356/A356643.seq
27f1e3308bf7a79e35d7eeba064db260
A356644
Number of vertex cuts in the n-antiprism graph.
[ "0", "0", "3", "48", "360", "2057", "10276", "47552", "209871", "898168", "3765080", "15560725", "63681228", "258826128", "1046920155", "4220390592", "16973219016", "68148598817", "273305152756", "1095189435488", "4386195036135", "17559755662600", "70280167711928", "281233465458733", "1125242449638300", "4501812479503152" ]
[ "nonn" ]
37
1
3
[ "A286183", "A356644" ]
null
Eric W. Weisstein, Aug 19 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356644.seq
00d0b77bf1fb9f600901c155d72abe77
A356645
a(n) = tau(n)^2 - 4*n^11 where tau is Ramanujan's tau function A000594.
[ "-3", "-7616", "-645084", "-14610432", "-171983600", "-1414609920", "-7628945436", "-27222867968", "-112609506987", "-386562553600", "-855436691900", "-2834434031616", "-6834860379504", "-16036772433920", "-33117544971900", "-69394306695168", "-89395660818176", "-249634755002304", "-352295159176476", "-768651312742400" ]
[ "sign" ]
6
1
1
[ "A000594", "A008455", "A356645" ]
null
Michel Marcus, Aug 19 2022
2022-08-19T13:52:49
oeisdata/seq/A356/A356645.seq
a202a5519f5ceb61885bb457a1160fc1
A356646
Numbers k such that the integer log of k! is a perfect power.
[ "4", "8", "27", "31", "575", "669", "1201", "2505", "4784", "7618", "35710", "65005", "166422", "870062", "994086", "1105670", "1209538", "2140133", "3020610", "9147713", "9404277", "14492743", "16792162", "18566766", "19445469", "21264479", "46483343", "109424090", "292374429", "293351547", "362681674", "399576585", "450622855" ]
[ "nonn" ]
20
1
1
[ "A001414", "A001597", "A025281", "A356631", "A356646" ]
null
J. M. Bergot and Robert Israel, Aug 19 2022
2022-08-30T22:08:32
oeisdata/seq/A356/A356646.seq
1092db5780d956181cf74d6ca397f2b0
A356647
Concatenation of runs {y..x} for each x>=1, using each y from 1 to x before moving on to the next value for x.
[ "1", "1", "2", "2", "1", "2", "3", "2", "3", "3", "1", "2", "3", "4", "2", "3", "4", "3", "4", "4", "1", "2", "3", "4", "5", "2", "3", "4", "5", "3", "4", "5", "4", "5", "5", "1", "2", "3", "4", "5", "6", "2", "3", "4", "5", "6", "3", "4", "5", "6", "4", "5", "6", "5", "6", "6", "1", "2", "3", "4", "5", "6", "7", "2", "3", "4", "5", "6", "7", "3", "4", "5", "6", "7", "4", "5", "6", "7", "5", "6", "7", "6", "7", "7", "1", "2", "3" ]
[ "nonn", "easy" ]
42
1
3
[ "A000120", "A004006", "A087118", "A356647" ]
null
Jonathan Kal-El Peréz, Aug 19 2022
2023-02-27T22:51:42
oeisdata/seq/A356/A356647.seq
ced86654b1fe2009ca5c1cec95db6c44
A356648
Numbers whose square is of the form k + reversal of digits of k, for some k.
[ "2", "4", "11", "22", "25", "33", "101", "121", "141", "202", "222", "264", "303", "307", "451", "836", "1001", "1111", "1221", "1232", "2002", "2068", "2112", "2222", "2305", "2515", "2626", "2636", "2776", "3003", "3958", "3972", "4015", "4081", "7975", "8184", "9757", "10001", "10201", "10401", "11011", "11121", "11211", "12012", "12021", "12221", "13046", "16581", "20002" ]
[ "nonn", "base" ]
56
1
1
[ "A056964", "A061230", "A067030", "A356648", "A358880", "A358984" ]
null
Nicolay Avilov, data a(10)-a(37) from Oleg Sorokin, Dec 10 2022
2023-03-15T10:55:56
oeisdata/seq/A356/A356648.seq
d65a23c205e7c5a5a74300310847afb7
A356649
Domination number of the Cartesian product of three n-cycles.
[ "1", "2", "5", "12", "20", "36", "49" ]
[ "nonn", "hard", "more" ]
11
1
2
[ "A094087", "A356649" ]
null
Richard Bean, Aug 19 2022
2022-10-02T00:44:50
oeisdata/seq/A356/A356649.seq
f56b69b0c3fe4fec935c1519ccea94f5
A356650
Domination number of the Cartesian product of four n-cycles.
[ "1", "4", "9", "32" ]
[ "hard", "more", "nonn" ]
10
1
2
[ "A094087", "A356650" ]
null
Richard Bean, Aug 20 2022
2022-10-02T00:44:59
oeisdata/seq/A356/A356650.seq
2ecd42569a308a7b9c724e0dcb1cf87e
A356651
Triangle read by rows. T(n, k) = [x^k](0^n + 4^n * ((1 - x)^(-1/2) - 1)).
[ "1", "0", "2", "0", "8", "6", "0", "32", "24", "20", "0", "128", "96", "80", "70", "0", "512", "384", "320", "280", "252", "0", "2048", "1536", "1280", "1120", "1008", "924", "0", "8192", "6144", "5120", "4480", "4032", "3696", "3432", "0", "32768", "24576", "20480", "17920", "16128", "14784", "13728", "12870", "0", "131072", "98304", "81920", "71680", "64512", "59136", "54912", "51480", "48620" ]
[ "nonn", "tabl" ]
10
0
3
[ "A000984", "A004171", "A172060", "A356651", "A357012" ]
null
Peter Luschny, Sep 08 2022
2022-09-09T04:06:21
oeisdata/seq/A356/A356651.seq
45bca70821c96ee2501dec547ec6fd4b
A356652
Triangle read by rows. Numerators of the coefficients of a sequence of rational polynomials r_n(x) with r_n(1) = B(2*n), where B(n) are the Bernoulli numbers.
[ "1", "0", "1", "0", "1", "-1", "0", "1", "-1", "5", "0", "1", "-41", "14", "-140", "0", "1", "-23", "93", "-40", "100", "0", "1", "-157", "2948", "-3652", "7700", "-15400", "0", "1", "-341", "18759", "-1937936", "520520", "-280280", "1401400", "0", "1", "-1927", "3478", "-7384676", "4364360", "-1430000", "5605600", "-8008000" ]
[ "sign", "frac", "tabl" ]
10
0
10
[ "A000367", "A002445", "A269941", "A356652", "A356653" ]
null
Peter Luschny, Sep 02 2022
2022-09-02T08:00:39
oeisdata/seq/A356/A356652.seq
8c8c59e2588c54193bfbfa4c5fffb154
A356653
Triangle read by rows. Denominators of the coefficients of a sequence of rational polynomials r_n(x) with r_n(1) = B(2*n), where B(n) are the Bernoulli numbers.
[ "1", "1", "6", "1", "70", "21", "1", "434", "31", "93", "1", "2286", "1905", "127", "1143", "1", "11242", "1533", "511", "73", "219", "1", "53222", "14329", "10235", "2047", "2047", "6141", "1", "245730", "40955", "40955", "368595", "24573", "8191", "73719", "1", "1114078", "294903", "4681", "491505", "42129", "4681", "14043", "42129" ]
[ "nonn", "frac", "tabl" ]
11
0
3
[ "A269941", "A356652", "A356653" ]
null
Peter Luschny, Sep 02 2022
2022-09-02T08:00:30
oeisdata/seq/A356/A356653.seq
9174545d241be02a3d2c2e5d92044c39
A356654
Triangle read by rows. T(n, k) = k! * Sum_{j=k..n} Lah(n, j) * Stirling2(j, k), where Lah(n, k) = A271703(n, k).
[ "1", "0", "1", "0", "3", "2", "0", "13", "18", "6", "0", "73", "158", "108", "24", "0", "501", "1510", "1590", "720", "120", "0", "4051", "15962", "23040", "15960", "5400", "720", "0", "37633", "186270", "345786", "325920", "168000", "45360", "5040", "0", "394353", "2385182", "5469492", "6579384", "4594800", "1884960", "423360", "40320" ]
[ "nonn", "tabl" ]
8
0
5
[ "A000262", "A048993", "A052838", "A084358", "A225479", "A271703", "A356654" ]
null
Peter Luschny, Sep 01 2022
2022-09-01T17:29:13
oeisdata/seq/A356/A356654.seq
54d1e332d27eacb07b2a95527aae3291
A356655
Clausen numbers based on the strictly proper divisors of n, 1 < d < n.
[ "1", "1", "1", "1", "3", "1", "3", "1", "15", "1", "3", "1", "105", "1", "3", "1", "15", "1", "21", "1", "165", "1", "3", "1", "1365", "1", "3", "1", "15", "1", "231", "1", "255", "1", "3", "1", "25935", "1", "3", "1", "165", "1", "21", "1", "345", "1", "3", "1", "23205", "1", "33", "1", "15", "1", "399", "1", "435", "1", "3", "1", "465465", "1", "3", "1", "255", "1", "483", "1", "15", "1", "33", "1" ]
[ "nonn" ]
14
0
5
[ "A160014", "A166120", "A356655" ]
null
Peter Luschny, Aug 20 2022
2022-08-21T06:13:03
oeisdata/seq/A356/A356655.seq
98e90365680ad6c1693b68de0cf35044
A356656
Partition triangle read by rows. The coefficients of the incomplete Bell polynomials.
[ "1", "0", "1", "0", "1", "1", "0", "1", "3", "1", "0", "1", "4", "3", "6", "1", "0", "1", "5", "10", "10", "15", "10", "1", "0", "1", "6", "15", "10", "15", "60", "15", "20", "45", "15", "1", "0", "1", "7", "21", "35", "21", "105", "70", "105", "35", "210", "105", "35", "105", "21", "1", "0", "1", "8", "28", "56", "35", "28", "168", "280", "210", "280", "56", "420", "280", "840", "105", "70", "560", "420", "56", "210", "28", "1" ]
[ "nonn", "tabf" ]
11
0
9
[ "A000110", "A036040", "A048993", "A052810", "A080575", "A132393", "A178867", "A356656" ]
null
Peter Luschny, Aug 28 2022
2022-08-28T16:57:36
oeisdata/seq/A356/A356656.seq
898df046baf4cefae4e8b35cec0a39a3
A356657
Numbers k that can be written as the sum of 8 divisors of k (not necessarily distinct).
[ "8", "10", "12", "14", "16", "18", "20", "22", "24", "26", "28", "30", "32", "36", "40", "42", "44", "48", "50", "52", "54", "56", "60", "64", "66", "68", "70", "72", "76", "78", "80", "84", "88", "90", "96", "98", "100", "102", "104", "108", "110", "112", "114", "120", "126", "128", "130", "132", "136", "138", "140", "144", "150", "152", "154", "156", "160", "162", "168", "170", "174", "176" ]
[ "nonn" ]
21
1
1
[ "A000027", "A299174", "A354591", "A355200", "A355641", "A356609", "A356635", "A356657", "A356659", "A356660" ]
null
Wesley Ivan Hurt, Aug 20 2022
2022-09-04T12:28:00
oeisdata/seq/A356/A356657.seq
5216a992f7f048aec7ae819f4e196807
A356658
The number of orderings of the hypercube Q_n whose disorder number is equal to the disorder number of Q_n.
[ "2", "8", "48", "2304", "4024320" ]
[ "nonn", "more" ]
9
1
1
[ "A271771", "A356658" ]
null
Sela Fried, Aug 20 2022
2022-09-11T09:30:28
oeisdata/seq/A356/A356658.seq
2f0bce71eb5f9fdad29a0ed33344cf05
A356659
Numbers k that can be written as the sum of 9 divisors of k (not necessarily distinct).
[ "9", "10", "12", "14", "15", "16", "18", "20", "21", "22", "24", "25", "26", "27", "28", "30", "32", "33", "35", "36", "39", "40", "42", "44", "45", "48", "50", "51", "52", "54", "55", "56", "57", "60", "63", "64", "65", "66", "68", "70", "72", "75", "76", "77", "78", "80", "81", "84", "85", "88", "90", "92", "96", "98", "99", "100", "102", "104", "105", "108", "110", "112", "114", "117", "120", "125" ]
[ "nonn" ]
15
1
1
[ "A000027", "A299174", "A354591", "A355200", "A355641", "A356609", "A356635", "A356657", "A356659", "A356660" ]
null
Wesley Ivan Hurt, Aug 20 2022
2022-10-09T09:42:18
oeisdata/seq/A356/A356659.seq
0563a71c8eff1fa4446929974b892ec2
A356660
Numbers k that can be written as the sum of 10 divisors of k (not necessarily distinct).
[ "10", "12", "14", "16", "18", "20", "22", "24", "26", "28", "30", "32", "34", "36", "40", "42", "44", "48", "50", "52", "54", "56", "60", "64", "66", "68", "70", "72", "76", "78", "80", "84", "88", "90", "92", "96", "98", "100", "102", "104", "108", "110", "112", "114", "116", "120", "126", "128", "130", "132", "136", "138", "140", "144", "150", "152", "154", "156", "160", "162" ]
[ "nonn" ]
24
1
1
[ "A000027", "A299174", "A354591", "A355200", "A355641", "A356609", "A356635", "A356657", "A356659", "A356660" ]
null
Wesley Ivan Hurt, Aug 20 2022
2022-10-09T09:42:22
oeisdata/seq/A356/A356660.seq
19dc8c7c34496bbf5c3828e0cba1413b
A356661
a(n) = n! * Sum_{d|n} 1/d^(n/d - 1).
[ "1", "4", "12", "60", "240", "1860", "10080", "95760", "766080", "8210160", "79833600", "1100484000", "12454041600", "188172784800", "2683799838720", "44951306400000", "711374856192000", "13745322470880000", "243290200817664000", "5142812718440517120", "103294640229580800000", "2351280996859354560000" ]
[ "nonn" ]
13
1
2
[ "A087905", "A087909", "A098558", "A356661", "A356662" ]
null
Seiichi Manyama, Aug 21 2022
2022-08-21T09:26:47
oeisdata/seq/A356/A356661.seq
d6644ac39fbcd98b0dcda8afc562fbe4
A356662
a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1).
[ "1", "4", "12", "60", "240", "1740", "10080", "87360", "735840", "7514640", "79833600", "976686480", "12454041600", "175736040480", "2616448554720", "42011071502400", "711374856192000", "12830610027755520", "243290200817664000", "4870565189425615680", "102182981410948838400", "2249099140674523737600" ]
[ "nonn" ]
13
1
2
[ "A061095", "A098558", "A356543", "A356661", "A356662" ]
null
Seiichi Manyama, Aug 21 2022
2022-08-21T09:26:51
oeisdata/seq/A356/A356662.seq
128dda36608b04a0522e693ae847679e
A356663
Number of ways to create an angle excess of n degrees using 3 distinct regular polygons with integral internal angles.
[ "0", "1", "3", "1", "3", "5", "1", "3", "4", "5", "2", "7", "2", "5", "6", "4", "2", "6", "2", "4", "5", "4", "2", "5", "4", "4", "6", "5", "2", "7", "2", "5", "6", "4", "6", "7", "4", "6", "9", "7", "5", "9", "6", "9", "9", "8", "6", "10", "6", "7", "8", "6", "6", "8", "6", "5", "7", "6", "4", "10", "3", "7", "7", "7", "7", "10", "6", "6", "10", "9", "7", "9", "6", "9", "11", "10", "7", "10" ]
[ "nonn" ]
15
1
3
[ "A356444", "A356663" ]
null
Joseph C. Y. Wong, Aug 21 2022
2022-10-02T00:43:30
oeisdata/seq/A356/A356663.seq
7703cca76f0eb55893aaf8cf5e176aac
A356664
Numbers k such that A225205(k) is in A354549.
[ "0", "2", "4", "10", "12", "14", "18", "20", "22", "30", "32", "34", "38", "40", "44", "48", "52", "60", "62", "72", "76", "78", "80", "82", "92", "94", "100", "104", "116", "120", "126", "130", "132", "134", "138", "140", "142", "144", "146", "148", "152", "154", "156", "158", "160", "168", "176", "180", "182", "186", "188", "192", "194", "202", "210", "222", "224", "226", "228", "230", "232" ]
[ "nonn" ]
14
1
2
[ "A001622", "A225204", "A225205", "A354513", "A354549", "A356591", "A356664" ]
null
Jianing Song, Aug 21 2022
2022-08-28T08:28:59
oeisdata/seq/A356/A356664.seq
acdd2a5d51dee6e53382c2277ede1991
A356665
Number of correct decimal digits of the approximation of Pi obtained from the continued fraction convergents A002485(n)/A002486(n).
[ "1", "3", "5", "7", "10", "10", "10", "10", "12", "11", "13", "13", "15", "16", "16", "17", "18", "18", "19", "20", "22", "24", "25", "25", "26", "28", "30", "31", "31", "33", "34", "35", "38", "40", "41", "41", "42", "43", "45", "46", "46", "47", "48", "50", "51", "52", "52", "54", "55", "56", "56", "57", "57", "59", "60", "60", "61", "61", "62", "61", "63", "65", "64" ]
[ "nonn", "base", "easy" ]
34
2
2
[ "A000796", "A002485", "A002486", "A356665" ]
null
Daniel Mondot, Aug 21 2022
2023-01-01T17:14:44
oeisdata/seq/A356/A356665.seq
31f675e59e770bb3be524f857917d06c
A356666
Smallest m such that the m-th Lucas number has exactly n divisors that are also Lucas numbers.
[ "1", "0", "3", "6", "15", "30", "45", "90", "105", "210", "405", "810", "315", "630", "3645", "2025", "945", "1890", "1575", "3150", "2835", "5670", "36450", "25025", "3465", "6930", "101250", "11025", "22050", "51030", "14175", "28350", "10395", "20790", "2952450", "175175", "17325", "34650", "1937102445", "625625", "31185", "62370", "127575", "255150" ]
[ "nonn" ]
19
1
3
[ "A000032", "A038547", "A102460", "A105802", "A304092", "A356123", "A356666" ]
null
Michel Marcus, Aug 22 2022
2022-09-04T12:35:44
oeisdata/seq/A356/A356666.seq
51c04d1629c0d62fb4b772071837210f
A356667
Expansion of e.g.f. Sum_{k>=0} x^k / (1 - k*x^k/k!).
[ "1", "1", "4", "12", "72", "240", "2520", "10080", "127680", "816480", "11037600", "79833600", "1514177280", "12454041600", "261655954560", "2699348652000", "62869385779200", "711374856192000", "19407798693803520", "243290200817664000", "7300765959334848000", "102980278869910041600" ]
[ "nonn" ]
16
0
3
[ "A356632", "A356633", "A356634", "A356667", "A356668" ]
null
Seiichi Manyama, Aug 22 2022
2022-08-22T10:06:07
oeisdata/seq/A356/A356667.seq
925d3385933f19c13b3a861edb1caf69
A356668
Expansion of e.g.f. Sum_{k>=0} x^k / (k! - k*x^k).
[ "1", "1", "3", "7", "37", "121", "1141", "5041", "60761", "378001", "5444461", "39916801", "729041545", "6227020801", "130767460825", "1321314894901", "31388220966961", "355687428096001", "9636906872926477", "121645100408832001", "3649432697160095561", "51223991519836175041", "1686001091666419279753" ]
[ "nonn" ]
15
0
3
[ "A038507", "A327578", "A356029", "A356328", "A356608", "A356667", "A356668" ]
null
Seiichi Manyama, Aug 22 2022
2022-08-22T10:06:03
oeisdata/seq/A356/A356668.seq
e450365496b840010706fc9d8e7246ff
A356669
The number of controllable graphs on n vertices.
[ "1", "0", "0", "0", "0", "8", "92", "2332", "85036", "5578994" ]
[ "nonn", "hard", "more" ]
12
1
6
[ "A356669", "A371897" ]
null
R. J. Mathar, Aug 22 2022
2024-04-11T18:09:31
oeisdata/seq/A356/A356669.seq
859571e7e488533a20d677bf26b9fd0f
A356670
a(n) is the number of correct decimal digits of Pi obtained from the fraction A355622(n)/A355623(n).
[ "0", "2", "3", "2", "4", "4", "7", "8", "8", "10", "10", "11", "11", "14", "14", "15", "16", "18", "18", "18", "19", "20", "22" ]
[ "nonn", "base", "more" ]
23
1
2
[ "A000796", "A355622", "A355623", "A356670", "A356671" ]
null
Stefano Spezia, Aug 22 2022
2022-10-13T10:58:41
oeisdata/seq/A356/A356670.seq
c5408293f6a85ee5682540b0bd5e2e78
A356671
Positive integers k such that A356670(k) = k.
[ "2", "7", "8", "10", "14", "18", "22" ]
[ "nonn", "more" ]
9
1
1
[ "A356670", "A356671" ]
null
Stefano Spezia, Aug 22 2022
2022-10-13T10:58:37
oeisdata/seq/A356/A356671.seq
b50307ac4dbc47f9f7a731bdc1f820fc
A356672
a(n) = n! * Sum_{k=0..n} k^(2*(n-k))/k!.
[ "1", "1", "3", "19", "253", "5661", "188191", "8983423", "594848409", "52174034713", "5852229698971", "822684190381131", "142739480367287893", "30074750245383836149", "7575373641076070706423", "2252600759590927171373431", "783103569459739402827046321", "315587346190678252431713684913" ]
[ "nonn" ]
9
0
3
[ "A234568", "A354436", "A356628", "A356672", "A356673" ]
null
Seiichi Manyama, Aug 22 2022
2022-08-22T14:28:48
oeisdata/seq/A356/A356672.seq
a8d623038069a2daa154d06ba0dc348e
A356673
a(n) = n! * Sum_{k=0..n} k^(3*(n-k))/k!.
[ "1", "1", "3", "31", "901", "45741", "3960871", "584698843", "130554106761", "40790044059481", "17681098707667531", "10491554658622447191", "8198225417359164798733", "8172446419302496167191941", "10264848632098736708582150511" ]
[ "nonn" ]
14
0
3
[ "A349880", "A354436", "A356629", "A356672", "A356673", "A358687" ]
null
Seiichi Manyama, Aug 22 2022
2022-11-27T06:44:31
oeisdata/seq/A356/A356673.seq
c9b7b7c62fbefdd81c633b55e6fda174
A356674
a(n) = n! * Sum_{k=0..n} k^(k*(n-k))/k!.
[ "1", "2", "5", "25", "349", "19941", "4440391", "4382699203", "17687865017481", "356274213630958297", "33338407933090938442411", "16214021627369697901867402911", "43817834057167927861655409052462093", "595284492835035398061242850538179192931525" ]
[ "nonn" ]
15
0
2
[ "A327578", "A349893", "A354436", "A356672", "A356673", "A356674" ]
null
Seiichi Manyama, Aug 22 2022
2022-11-27T05:12:41
oeisdata/seq/A356/A356674.seq
039bee9a383e22e90f5cb8e967bd29e1
A356675
Lexicographically earliest infinite sequence satisfying a(1) > -1 and a(n-1) = A075826(a(n)).
[ "1", "5", "9", "16", "27", "38", "48", "58", "66", "76", "87", "98", "117", "136", "155", "177", "198", "215", "235", "254", "275", "295", "310", "333", "350", "372", "394", "411", "433", "452", "474", "495", "514", "535", "555", "576", "598", "615", "635", "650", "669", "689", "705", "728", "749", "773", "795", "810", "833", "850", "872", "894", "913", "934", "950", "973", "994", "1013", "1034", "1050", "1071", "1093" ]
[ "nonn", "word" ]
47
1
2
[ "A005589", "A075826", "A356675" ]
null
Aidan Clarke, Aug 22 2022
2022-11-26T09:38:28
oeisdata/seq/A356/A356675.seq
f9503e74a5cc9f7aa6a511cd0c65a46d
A356676
A certain morphism applied to A007814 that is related to the lexicographically least infinite squarefree words over the nonnegative integers.
[ "0", "1", "0", "2", "0", "3", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "2", "0" ]
[ "nonn" ]
21
1
4
[ "A007814", "A356676", "A356677", "A356679" ]
null
Joey Lakerdas-Gayle, Aug 22 2022
2022-11-27T09:02:56
oeisdata/seq/A356/A356676.seq
cc4c5b65b53fb1812ecc35362e94e3c4
A356677
The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 1.
[ "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "3", "0", "1", "0", "3", "0", "2", "0", "1", "0", "2", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "3", "0", "1", "0", "3", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "2", "3", "0", "1", "0" ]
[ "nonn" ]
43
1
4
[ "A007814", "A356676", "A356677", "A356678", "A356679", "A356680", "A356681", "A356682" ]
null
Joey Lakerdas-Gayle, Aug 22 2022
2022-11-27T09:02:48
oeisdata/seq/A356/A356677.seq
5727ce1e6bbee99b56386db3efce5639
A356678
The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 2.
[ "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "2", "0", "1", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2" ]
[ "nonn" ]
24
1
1
[ "A007814", "A356677", "A356678", "A356679", "A356680", "A356681", "A356682" ]
null
Joey Lakerdas-Gayle, Aug 22 2022
2023-01-03T01:27:41
oeisdata/seq/A356/A356678.seq
ee96b1a75e3e216c3b304c46dc2932b6
A356679
The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 3.
[ "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "2", "0", "1", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0" ]
[ "nonn" ]
17
1
1
[ "A007814", "A356676", "A356677", "A356678", "A356679", "A356680", "A356681", "A356682" ]
null
Joey Lakerdas-Gayle, Oct 18 2022
2022-11-28T12:20:00
oeisdata/seq/A356/A356679.seq
cac6cfaf46fca25ee1274c788b0b6833
A356680
The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 1, 2.
[ "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "3", "0", "1", "0", "3", "0", "2", "0", "1", "0", "2", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "3", "0", "1", "0", "3", "0", "2", "0", "1", "2", "0", "2", "1" ]
[ "nonn" ]
17
1
2
[ "A007814", "A356677", "A356678", "A356679", "A356680", "A356681", "A356682" ]
null
Joey Lakerdas-Gayle, Oct 18 2022
2023-01-03T00:47:43
oeisdata/seq/A356/A356680.seq
12275e67d19644de54a08a397ef0314c
A356681
The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 1, 3.
[ "1", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1" ]
[ "nonn" ]
15
1
2
[ "A007814", "A356677", "A356678", "A356679", "A356680", "A356681", "A356682" ]
null
Joey Lakerdas-Gayle, Oct 18 2022
2023-01-03T01:27:14
oeisdata/seq/A356/A356681.seq
57b7d56358ae9731f872f1f27ad0900f
A356682
The lexicographically earliest infinite squarefree sequence of nonnegative integers that starts with 2, 1.
[ "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "0", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "1", "2", "1", "0", "1", "2", "0", "1", "0", "2", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "3", "0", "1", "0", "3", "0", "2", "0", "1", "0", "2", "0", "3", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "3", "0", "1", "0", "3", "1", "0", "1", "2", "0", "1", "0", "2" ]
[ "nonn" ]
15
1
1
[ "A007814", "A356677", "A356678", "A356679", "A356680", "A356681", "A356682" ]
null
Joey Lakerdas-Gayle, Oct 18 2022
2023-01-03T09:26:04
oeisdata/seq/A356/A356682.seq
5a668b95437989e936edde5432c51b26
A356683
a(n) is the smallest positive k such that the count of squarefree numbers <= k that have n prime factors is equal to the count of squarefree numbers <= k that have n-1 prime factors (and the count is positive).
[ "2", "39", "1279786", "8377774397163159586" ]
[ "nonn", "bref", "hard", "more" ]
51
1
1
[ "A000040", "A005117", "A006881", "A007304", "A046386", "A046387", "A067885", "A072047", "A115343", "A123321", "A123322", "A281222", "A340316", "A356683" ]
null
Jon E. Schoenfield, Nov 22 2022
2025-01-31T17:23:48
oeisdata/seq/A356/A356683.seq
7dcd9fcf3dd9b7643542dd3e7b782da4
A356684
a(n) = (n-1)*a(n-1) - n*a(n-2), with a(1) = a(2) = -1.
[ "-1", "-1", "1", "7", "23", "73", "277", "1355", "8347", "61573", "523913", "5024167", "53479135", "624890417", "7946278813", "109195935523", "1612048228547", "25439293045885", "427278358483537", "7609502950269503", "143217213477235783", "2840152418116022377" ]
[ "sign", "easy" ]
21
1
4
[ "A051403", "A356247", "A356684" ]
null
Mohammed Bouras, Aug 22 2022
2023-06-05T07:36:53
oeisdata/seq/A356/A356684.seq
96973dc6378e49b29b24f575f69b1740
A356685
Number of inequivalent simultaneous colorings of the faces, vertices and edges of the cube under rotational symmetry using at most n colors.
[ "1", "2802752", "105912891117", "187650085502976", "62088173933203125", "7107572036889562176", "391145014323085681337", "12592977289302016786432", "269211745393024690982601", "4166666666704170025000000" ]
[ "nonn", "easy" ]
20
1
2
[ "A355502", "A356685" ]
null
Marko Riedel, Aug 22 2022
2022-08-24T09:31:33
oeisdata/seq/A356/A356685.seq
20e3744b873acb11280f85f5dc19e793
A356686
Decimal expansion of the constant p^*_0 related to Shallit's constant (A086276).
[ "1", "4", "4", "7", "0", "5", "4", "3", "5", "0", "0", "1", "6", "2", "7", "9", "4", "0", "6", "5", "6", "4", "3", "6", "5", "3", "2", "0", "2", "2", "3", "2", "2", "1", "5", "0", "1", "3", "4", "5", "1", "1", "4", "7", "7", "6", "6", "0", "9", "9", "6", "3", "3", "5", "4", "1", "9", "1", "1", "6", "0", "4", "2", "6", "0", "9", "2", "8", "8", "8", "4", "5", "9", "4", "9", "5", "5", "3", "8", "1", "5" ]
[ "nonn", "cons" ]
17
1
2
[ "A086276", "A356686" ]
null
Georg Fischer, Aug 23 2022
2022-08-25T08:58:21
oeisdata/seq/A356/A356686.seq
cc3fe46f315efbc4b04435add6c8a150
A356687
a(n) = n! * Sum_{k=0..n} k^(2*n)/k!.
[ "1", "1", "18", "927", "94876", "16251045", "4210190766", "1543550310211", "764096247603480", "493254380867214249", "404269328278061434810", "411862088865696890314311", "512690851568229926690616948", "768775988931240685277619894157" ]
[ "nonn" ]
17
0
3
[ "A030297", "A249459", "A256016", "A356672", "A356687", "A356688" ]
null
Seiichi Manyama, Aug 23 2022
2022-08-24T12:09:11
oeisdata/seq/A356/A356687.seq
904eceb18645f886d7263f930e059892
A356688
a(n) = n! * Sum_{k=0..n} k^(3*n)/k!.
[ "1", "1", "66", "21225", "18952156", "36175231585", "126556309395486", "733064060959310689", "6540867625730306094360", "85180334386943946887707617", "1552697061493449955344530003290", "38315904135534199560725372265381721", "1245605749857294018587318829355458646068" ]
[ "nonn" ]
16
0
3
[ "A256016", "A337001", "A349901", "A356673", "A356687", "A356688" ]
null
Seiichi Manyama, Aug 23 2022
2022-08-24T12:09:20
oeisdata/seq/A356/A356688.seq
876516c0556c25de524072f940604ed2
A356689
a(n) = n! * Sum_{k=0..n} k^(k*n)/k!.
[ "1", "2", "20", "19887", "4297096180", "298028721722131825", "10314430386434427534836297166", "256923580889667624113335512704714686054849", "6277101737079381675512518990977258744796239498871290255000" ]
[ "nonn" ]
13
0
2
[ "A256016", "A349886", "A356674", "A356687", "A356688", "A356689" ]
null
Seiichi Manyama, Aug 23 2022
2022-09-17T08:44:42
oeisdata/seq/A356/A356689.seq
0058c284f93fe21ab1ba07d769db88fd
A356690
Product of the prime numbers that are between 10*n and 10*(n+1).
[ "210", "46189", "667", "1147", "82861", "3127", "4087", "409457", "7387", "97", "121330189", "113", "127", "2494633", "149", "23707", "27221", "30967", "181", "1445140189", "1", "211", "11592209", "55687", "241", "64507", "70747", "75067", "79523", "293", "307", "30857731", "1", "111547", "121103", "126727", "367", "141367", "148987", "397", "164009", "419", "421" ]
[ "nonn", "easy" ]
45
0
1
[ "A000040", "A000720", "A032352", "A179816", "A216292", "A356690" ]
null
Hemjyoti Nath, Aug 23 2022
2022-09-30T16:30:08
oeisdata/seq/A356/A356690.seq
e420672345be63a689f20546ac0cf6ec
A356691
a(n) = n! * Sum_{k=0..n} k^(2*k)/k!.
[ "1", "2", "20", "789", "68692", "10109085", "2237436846", "693885130771", "287026057756824", "152677869816810537", "101526778698168105370", "82519543952519610272391", "80487081730821079456710228", "92779662255769290691336848973", "124775610962828705895908497741878" ]
[ "nonn" ]
14
0
2
[ "A062206", "A277506", "A350008", "A356689", "A356691" ]
null
Seiichi Manyama, Aug 23 2022
2022-08-23T09:41:10
oeisdata/seq/A356/A356691.seq
d16211e2f32d7d8a9bca2ad55ac6fe5f
A356692
Pascal-like triangle, where each entry is the sum of the four entries above it starting with 1 at the top.
[ "1", "1", "1", "2", "2", "2", "4", "6", "6", "4", "10", "16", "20", "16", "10", "26", "46", "62", "62", "46", "26", "72", "134", "196", "216", "196", "134", "72", "206", "402", "618", "742", "742", "618", "402", "206", "608", "1226", "1968", "2504", "2720", "2504", "1968", "1226", "608", "1834", "3802", "6306", "8418", "9696", "9696", "8418", "6306", "3802", "1834", "5636", "11942", "20360", "28222", "34116", "36228", "34116", "28222", "20360", "11942", "5636" ]
[ "nonn", "tabl" ]
28
0
4
[ "A007318", "A064189", "A216837", "A356692", "A356832", "A356853" ]
null
Greg Dresden and Sadek Mohammed, Aug 23 2022
2022-09-03T22:08:23
oeisdata/seq/A356/A356692.seq
9e50b3944cd9d3eab8fe1b51402987aa
A356693
Decimal expansion of the constant B(2) = Sum_{n>=1} Sum_{m>=n+1} 1/(z(n)*z(m))^2 where z(n) is the imaginary part of the n-th nontrivial zero of the Riemann zeta function.
[ "0", "0", "0", "2", "4", "8", "3", "3", "4", "0", "5", "3", "7", "8", "9", "1", "4", "4", "1", "7", "5", "7", "2", "3", "8", "5", "6", "4", "4", "5", "2", "0", "8", "8", "1", "7", "7", "2", "6", "2", "0", "1", "4", "7", "6", "4", "7", "2", "5", "9", "8", "0", "2", "0", "3", "0", "7", "3", "3", "8", "1", "5", "4", "5", "2", "6", "0", "6", "7", "4", "9", "8", "3", "3", "2", "5", "1", "8", "3", "1", "4", "9", "0", "4", "6", "9", "7", "9", "2", "4", "0", "4", "8", "3", "7", "2", "0", "2", "3", "1", "7", "1", "9", "8", "2", "2", "2", "8", "7", "6", "5", "6", "9", "1", "7", "4", "5", "9" ]
[ "nonn", "cons" ]
26
0
4
[ "A013629", "A074760", "A104539", "A104540", "A104541", "A104542", "A245275", "A245276", "A306339", "A306340", "A306341", "A332645", "A333360", "A335814", "A335815", "A355283", "A356693" ]
null
Artur Jasinski, Aug 23 2022
2022-11-06T09:11:59
oeisdata/seq/A356/A356693.seq
1cc552ebabe048a808534f47660f18bd
A356694
Number of unrooted hypermaps of genus 4 with n darts.
[ "900", "58032", "2112300", "57017238", "1269067260", "24635879496", "431403755052", "6967561712925", "105413618746896", "1510962076238986", "20695115375890776", "272660503240047690", "3473773540061130158", "42978345198144175632", "518176854304561585680", "6105782484587260861256", "70484498508285180442512", "798783395497239872773008" ]
[ "nonn" ]
4
9
1
[ "A318104", "A356694" ]
null
R. J. Mathar, Aug 23 2022
2022-08-23T14:11:08
oeisdata/seq/A356/A356694.seq
8c03d5840d569599ee6d5b969abb489a
A356695
Expansion of x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5).
[ "1", "1", "2", "4", "10", "24", "53", "132", "310", "711", "1736", "4053", "9475", "22800", "53294", "125667", "299629", "702555", "1661861", "3941889", "9269716", "21941640", "51908768", "122325141", "289466629", "684020046", "1614034607", "3817513449", "9017274205", "21292938474", "50340109313", "118899240972" ]
[ "nonn", "easy" ]
14
1
3
[ "A131572", "A356695" ]
null
R. J. Mathar, Aug 23 2022
2023-04-20T18:14:32
oeisdata/seq/A356/A356695.seq
2f295f5f8c1c6e66070e8bff631dca5d
A356696
a(n) = Fibonacci(2n-1) - 2^n + binomial(n,2) + 2.
[ "2", "1", "1", "2", "5", "14", "42", "128", "384", "1123", "3204", "8955", "24629", "66913", "180127", "481568", "1280855", "3393644", "8965476", "23633702", "62197602", "163483201", "429300366", "1126514817", "2954438135", "7745187919", "20297902537", "53182073798", "139315427369", "364898425658", "955648284654" ]
[ "nonn", "easy" ]
25
0
1
[ "A000045", "A000108", "A000325", "A307464", "A307465", "A307466", "A356696" ]
null
R. J. Mathar, Aug 23 2022
2024-08-29T15:03:13
oeisdata/seq/A356/A356696.seq
be6e34116b55ba49da5d66e882dd1011
A356697
Number of Catalan words of length n avoiding the pattern 0000.
[ "1", "1", "2", "5", "13", "36", "101", "280", "788", "2212", "6186", "17384", "48755", "136649", "383584", "1075734", "3016924", "8464693", "23740844", "66592246", "186807727", "523973400", "1469769653", "4122833303", "11564436141", "32438795011", "90992182917", "255234015580", "715941436278", "2008237780651" ]
[ "nonn", "easy" ]
9
0
3
[ "A000108", "A307464", "A356697", "A356698" ]
null
Alois P. Heinz, Aug 23 2022
2022-08-25T08:49:11
oeisdata/seq/A356/A356697.seq
d65dbf576ddf73a28738a9a57c4b332c
A356698
Number of Catalan words of length n avoiding the pattern 00000.
[ "1", "1", "2", "5", "14", "41", "125", "389", "1220", "3829", "12091", "38237", "120869", "382000", "1208863", "3824981", "12098811", "38272739", "121105815", "383157721", "1212151630", "3835001361", "12133807832", "38388624860", "121452176437", "384255298818", "1215726271065", "3846304406380", "12168956318213" ]
[ "nonn", "easy" ]
8
0
3
[ "A000108", "A307464", "A356697", "A356698" ]
null
Alois P. Heinz, Aug 23 2022
2022-08-25T08:47:28
oeisdata/seq/A356/A356698.seq
59e61a6dd6dfbd5e5d0df26e0a3ec757
A356699
Numbers k such that Mordell's equation y^2 = x^3 + k has a record number of integral solutions.
[ "1", "8", "9", "17", "225", "1025" ]
[ "nonn", "hard", "more" ]
9
1
2
[ "A081119", "A081120", "A356699", "A356700", "A356701", "A356702" ]
null
Jianing Song, Aug 23 2022
2022-08-24T09:03:38
oeisdata/seq/A356/A356699.seq
a2b1efa517e9aaa451231993fe6729cf
A356700
Numbers k such that Mordell's equation y^2 = x^3 - k has a record number of integral solutions.
[ "1", "2", "4", "28", "116", "207", "431", "2351", "3807" ]
[ "nonn", "hard", "more" ]
34
1
2
[ "A081119", "A081120", "A356699", "A356700", "A356701", "A356702" ]
null
Jianing Song, Aug 23 2022
2024-08-15T03:46:40
oeisdata/seq/A356/A356700.seq
66070a3e2d409778ec4abcd2da44033f