A356529 a(n) = (n-1)! * Sum_{d|n} d^(n-d+1).
1, 3, 8, 78, 144, 14400, 5760, 5851440, 88583040, 5859786240, 43545600, 24077414592000, 6706022400, 35948640894566400, 4395744249613516800, 263312496059348736000, 376610217984000, 5901087844517892009984000, 128047474114560000
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := (n - 1)! * DivisorSum[n, #^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Aug 10 2022 *)
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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^k)))
Formula
a(n) = (n-1)! * A342675(n).
If p is prime, a(p) = (1+p) * (p-1)!.
E.g.f.: -Sum_{k>0} log(1 - (k * x)^k)/k^k.