A356486 a(n) = (n-1)! * Sum_{d|n} d^n / (d-1)!.
1, 5, 29, 358, 3149, 98196, 824263, 73122736, 784270089, 158028202000, 285315299411, 855386690484096, 302875585593853, 5876921233326141376, 111916280261483009775, 73985874496557113890816, 827240282809126652177, 1625215094103508198780449024
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := (n-1)! * DivisorSum[n, #^n / (#-1)! &]; Array[a, 18] (* Amiram Eldar, Aug 30 2023 *)
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PARI
a(n) = (n-1)!*sumdiv(n, d, d^n/(d-1)!);
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-(k*x)^k)/k!)))
Formula
If p is prime, a(p) = p^p + (p-1)!.
E.g.f.: -Sum_{k>0} log(1 - (k * x)^k)/k!.