A356486 - OEIS

%I #17 Aug 30 2023 02:00:40

%S 1,5,29,358,3149,98196,824263,73122736,784270089,158028202000,

%T 285315299411,855386690484096,302875585593853,5876921233326141376,

%U 111916280261483009775,73985874496557113890816,827240282809126652177,1625215094103508198780449024

%N a(n) = (n-1)! * Sum_{d|n} d^n / (d-1)!.

%F If p is prime, a(p) = p^p + (p-1)!.

%F E.g.f.: -Sum_{k>0} log(1 - (k * x)^k)/k!.

%t a[n_] := (n-1)! * DivisorSum[n, #^n / (#-1)! &]; Array[a, 18] (* _Amiram Eldar_, Aug 30 2023 *)

%o (PARI) a(n) = (n-1)!*sumdiv(n, d, d^n/(d-1)!);

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-(k*x)^k)/k!)))

%Y Cf. A087906, A354890, A356487.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Aug 09 2022