A354890
a(n) = n! * Sum_{d|n} d^n / d!.
Original entry on oeis.org
1, 6, 33, 472, 3245, 157896, 828583, 132078976, 1578211209, 307174074400, 285351587411, 1835340563252736, 302881333613053, 11743240652094910336, 336123967242674523375, 149825956013958069846016, 827240617573764860177, 3551697093896307129060647424
Offset: 1
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a[n_] := n! * DivisorSum[n, #^n/#! &]; Array[a, 18] (* Amiram Eldar, Jun 10 2022 *)
-
a(n) = n!*sumdiv(n, d, 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!*(1-(k*x)^k)))))
A354893
a(n) = n! * Sum_{d|n} d^(n - d) / (n/d)!.
Original entry on oeis.org
1, 3, 7, 73, 121, 12361, 5041, 5308801, 44452801, 5681370241, 39916801, 16800125569921, 6227020801, 35897693762810881, 2134168822456070401, 190139202281277849601, 355687428096001, 3563095308471181273190401, 121645100408832001
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(n - #)/(n/#)! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
-
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^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
-
a[n_] := n! * DivisorSum[n, #^n/(#! * (n/#)!) &]; Array[a, 18] (* Amiram Eldar, Jun 11 2022 *)
-
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!)))
A363698
a(n) = n! * Sum_{d|n} (-1)^(d+1) * (n/d)^n / d!.
Original entry on oeis.org
1, 7, 163, 5951, 375001, 33337559, 4150656721, 675135713279, 140588337476161, 36270281280965759, 11388728893445164801, 4270306368140557557119, 1886009588552176549862401, 968696203690612910273080319
Offset: 1
-
a[n_] := n! * DivisorSum[n, (-1)^(#+1) * (n/#)^n / #! &]; Array[a, 15] (* Amiram Eldar, Jul 03 2023 *)
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a(n) = n!*sumdiv(n, d, (-1)^(d+1)*(n/d)^n/d!);
A354900
a(n) = n! * Sum_{d|n} d^d / (n/d)!.
Original entry on oeis.org
1, 9, 163, 6193, 375001, 33602521, 4150656721, 676462516801, 140587148681281, 36288005670120961, 11388728893445164801, 4270826391670469473921, 1886009588552176549862401, 968725766890781857146309121, 572622616354852243874626732801
Offset: 1
-
a[n_] := n! * DivisorSum[n, #^#/(n/#)! &]; Array[a, 15] (* Amiram Eldar, Jun 11 2022 *)
-
a(n) = n!*sumdiv(n, d, d^d/(n/d)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1))))
A356495
Expansion of e.g.f. Product_{k>0} B((k * x)^k) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.
Original entry on oeis.org
1, 1, 10, 191, 7287, 424292, 37434683, 4512452023, 726390985036, 149098938941283, 38187088904721655, 11903871288193251930, 4442392007373264794677, 1953788894138983864638457, 1000334575509506861927067378, 589712001176601700420819946615
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp((k*x)^k)-1))))
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a354892(n) = n!*sumdiv(n, d, d^n/(n/d)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354892(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-6 of 6 results.