A354899 - OEIS

%I #14 Jun 11 2022 07:52:29

%S 1,5,28,281,3126,48517,823544,16995617,387692650,10047310481,

%T 285311670612,8932562801857,302875106592254,11119129387084097,

%U 437899615088648176,18451106376806703617,827240261886336764178,39349894934527426209025

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

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

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

%t a[n_] := n! * DivisorSum[n, #^#/(#! * (n/#)!) &]; Array[a, 18] (* _Amiram Eldar_, Jun 11 2022 *)

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

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

%Y Cf. A121860, A354844, A354888, A354897, A354900.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 11 2022