A354892
a(n) = n! * Sum_{d|n} d^n / (n/d)!.
Original entry on oeis.org
1, 9, 163, 6337, 375001, 33862441, 4150656721, 677778984961, 140588337476161, 36305718780965761, 11388728893445164801, 4271349071581227377281, 1886009588552176549862401, 968755330019156299208709121, 572622623006183707899105964801
Offset: 1
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a[n_] := n! * DivisorSum[n, #^n/(n/#)! &]; Array[a, 15] (* Amiram Eldar, Jun 10 2022 *)
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a(n) = n!*sumdiv(n, d, d^n/(n/d)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, exp((k*x)^k)-1)))
A354891
a(n) = n! * Sum_{d|n} d^(n - d) / d!.
Original entry on oeis.org
1, 3, 7, 73, 121, 9721, 5041, 1760641, 44452801, 562615201, 39916801, 3156125575681, 6227020801, 192873372531841, 222245415808416001, 14806216643368550401, 355687428096001, 34884164976924636172801, 121645100408832001
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(n - #)/#! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
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a(n) = n!*sumdiv(n, d, d^(n-d)/d!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!*(1-(k*x)^k)))))
A354897
a(n) = n! * Sum_{d|n} d^n / (d! * (n/d)!).
Original entry on oeis.org
1, 5, 28, 353, 3126, 94237, 823544, 72042497, 585825130, 157671732881, 285311670612, 790577855833537, 302875106592254, 5876819345289651137, 55890419425648520176, 73205730667453550166017, 827240261886336764178, 1474631675630757976051079425
Offset: 1
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a[n_] := n! * DivisorSum[n, #^n/(#! * (n/#)!) &]; Array[a, 18] (* Amiram Eldar, Jun 11 2022 *)
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a(n) = n!*sumdiv(n, d, d^n/(d!*(n/d)!));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp((k*x)^k)-1)/k!)))
A356486
a(n) = (n-1)! * Sum_{d|n} d^n / (d-1)!.
Original entry on oeis.org
1, 5, 29, 358, 3149, 98196, 824263, 73122736, 784270089, 158028202000, 285315299411, 855386690484096, 302875585593853, 5876921233326141376, 111916280261483009775, 73985874496557113890816, 827240282809126652177, 1625215094103508198780449024
Offset: 1
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a[n_] := (n-1)! * DivisorSum[n, #^n / (#-1)! &]; Array[a, 18] (* Amiram Eldar, Aug 30 2023 *)
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a(n) = (n-1)!*sumdiv(n, d, d^n/(d-1)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-(k*x)^k)/k!)))
A358595
a(n) = n! * Sum_{d|n} d^n / d!^(n/d).
Original entry on oeis.org
1, 6, 33, 376, 3245, 67716, 828583, 22050176, 420850809, 12580687900, 285351587411, 11736333558720, 302881333613053, 13450914411140584, 463402585399165875, 22345557703564558336, 827240617573764860177, 48442529220731147887020
Offset: 1
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a[n_] := n! * DivisorSum[n, #^n / #!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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a(n) = n!*sumdiv(n, d, d^n/d!^(n/d));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!-(k*x)^k))))
Showing 1-5 of 5 results.