A354897 a(n) = n! * Sum_{d|n} d^n / (d! * (n/d)!).
1, 5, 28, 353, 3126, 94237, 823544, 72042497, 585825130, 157671732881, 285311670612, 790577855833537, 302875106592254, 5876819345289651137, 55890419425648520176, 73205730667453550166017, 827240261886336764178, 1474631675630757976051079425
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, #^n/(#! * (n/#)!) &]; Array[a, 18] (* Amiram Eldar, Jun 11 2022 *)
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PARI
a(n) = n!*sumdiv(n, d, d^n/(d!*(n/d)!));
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp((k*x)^k)-1)/k!)))
Formula
E.g.f.: Sum_{k>0} (exp((k * x)^k) - 1)/k!.
If p is prime, a(p) = 1 + p^p.