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%I #17 Jun 11 2022 07:51:49
%S 1,6,33,328,3245,52056,828583,17328256,389416329,10105386400,
%T 285351587411,8955841614336,302881333613053,11126513414294656,
%U 437935136609883375,18455736024587862016,827240617573764860177,39353706314004951028224
%N a(n) = n! * Sum_{d|n} d^d / d!.
%H Seiichi Manyama, <a href="/A354888/b354888.txt">Table of n, a(n) for n = 1..386</a>
%F E.g.f.: Sum_{k>0} (k * x)^k/(k! * (1 - x^k)).
%F If p is prime, a(p) = p^p + p! = A053042(p).
%t a[n_] := n! * DivisorSum[n, #^#/#! &]; Array[a, 18] (* _Amiram Eldar_, Jun 10 2022 *)
%o (PARI) a(n) = n!*sumdiv(n, d, d^d/d!);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!*(1-x^k)))))
%Y Cf. A327579, A354843, A354889.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 10 2022
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