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
-
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!)))
A354338
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * (k/d)!) )/(n-k)!.
Original entry on oeis.org
1, 4, 12, 41, 145, 742, 3962, 27659, 215131, 1996356, 17300360, 218809109, 2421142269, 31105286682, 427776526574, 6964677268087, 97708052695959, 1856379196278120, 30362097934331500, 606395795174882161, 12016899266310773097, 261771941015999635310
Offset: 1
-
a087906(n) = n!*sumdiv(n, d, 1/(d*(n/d)!));
a(n) = sum(k=1, n, a087906(k)*binomial(n, k));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, (exp(x^k)-1)/k)))
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-x^k)/k!)))
A356575
Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k!) )^x.
Original entry on oeis.org
1, 0, 2, 6, 24, 185, 990, 9877, 72968, 824553, 8495560, 102689741, 1317098772, 18729163609, 270642677396, 4396374315075, 73997950572016, 1318896555293137, 24900891903482832, 499312682762581945, 10301544926241347140, 227464062944112566481
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(1/k!))^x))
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a087906(n) = (n-1)!*sumdiv(n, d, 1/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a087906(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
A363736
a(n) = (n-1)! * Sum_{d|n} (-1)^(d+1) / (d-1)!.
Original entry on oeis.org
1, 0, 3, -1, 25, 59, 721, -841, 60481, 15119, 3628801, 12972959, 479001601, 8648639, 134399865601, -218205187201, 20922789888001, 174888473759999, 6402373705728001, -15205972772390401, 3652732042831872001, 14079294028799, 1124000727777607680001
Offset: 1
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a[n_] := (n-1)! * DivisorSum[n, (-1)^(#+1)/(#-1)! &]; Array[a, 25] (* Amiram Eldar, Jul 03 2023 *)
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a(n) = (n-1)!*sumdiv(n, d, (-1)^(d+1)/(d-1)!);
A370608
a(n) = (n-1)! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).
Original entry on oeis.org
1, 2, 3, 10, 25, 156, 721, 5356, 40881, 366850, 3628801, 40048086, 479001601, 6228391456, 87184121025, 1307724593176, 20922789888001, 355689166978146, 6402373705728001, 121645161595446490, 2432902128489747201, 51090943465394571376, 1124000727777607680001
Offset: 1
-
a(n) = (n-1)!*sumdiv(n, d, 1/((d-1)!*(n/d)!^(d-1)));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k-1)!*(exp(x^k/k!)-1))))