login
a(n) = n! * Sum_{d|n} d^n / (d! * (n/d)!).
2

%I #15 Jun 11 2022 07:52:19

%S 1,5,28,353,3126,94237,823544,72042497,585825130,157671732881,

%T 285311670612,790577855833537,302875106592254,5876819345289651137,

%U 55890419425648520176,73205730667453550166017,827240261886336764178,1474631675630757976051079425

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

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

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

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

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

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

%Y Cf. A121860, A354844, A354890, A354892, A354893, A354898, A354899.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 11 2022