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%I #17 Jun 11 2022 07:52:03
%S 1,6,33,472,3245,157896,828583,132078976,1578211209,307174074400,
%T 285351587411,1835340563252736,302881333613053,11743240652094910336,
%U 336123967242674523375,149825956013958069846016,827240617573764860177,3551697093896307129060647424
%N a(n) = n! * Sum_{d|n} d^n / d!.
%H Seiichi Manyama, <a href="/A354890/b354890.txt">Table of n, a(n) for n = 1..284</a>
%F E.g.f.: Sum_{k>0} (k * x)^k/(k! * (1 - (k * x)^k)).
%F If p is prime, a(p) = p^p + p! = A053042(p).
%t a[n_] := n! * DivisorSum[n, #^n/#! &]; Array[a, 18] (* _Amiram Eldar_, Jun 10 2022 *)
%o (PARI) a(n) = n!*sumdiv(n, d, d^n/d!);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!*(1-(k*x)^k)))))
%Y Cf. A053042, A354888, A354891, A354892.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 10 2022
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