%I #19 Jun 11 2022 07:51:54

%S 1,4,15,112,745,10296,122689,2285312,43953921,1026157600,25977341401,

%T 751135431168,23304312143281,795924137531264,29203006015310625,

%U 1154107395053387776,48661547563094964481,2186762596692631699968,104127471943011650364841

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

%H Seiichi Manyama, <a href="/A354889/b354889.txt">Table of n, a(n) for n = 1..387</a>

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

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

%t a[n_] := n! * DivisorSum[n, #^(# - 1)/#! &]; Array[a, 19] (* _Amiram Eldar_, Jun 10 2022 *)

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

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

%Y Cf. A262843, A327578, A354845, A354888.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 10 2022