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%I #13 Jun 08 2022 14:23:39
%S 1,3,8,54,144,2880,5760,206640,1491840,24675840,43545600,10298534400,
%T 6706022400,1195587993600,33476463820800,775450900224000,
%U 376610217984000,553805325545472000,128047474114560000,339876410542276608000,6208765924866785280000
%N a(n) = (n-1)! * Sum_{d|n} d^(n/d).
%F a(n) = (n-1)! * A055225(n).
%F E.g.f.: -Sum_{k>0} log(1 - k * x^k)/k.
%F If p is prime, a(p) = (p-1)! + p!.
%t a[n_] := (n - 1)! * DivisorSum[n, #^(n/#) &]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2022 *)
%o (PARI) a(n) = (n-1)!*sumdiv(n, d, d^(n/d));
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)))
%Y Cf. A055225, A318249, A354848.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 08 2022
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