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%I #10 Jun 10 2022 11:07:59
%S 1,4,9,76,125,4686,5047,389768,1995849,62445610,39916811,23574862092,
%T 6227020813,5667436494734,55630647072015,2922249531801616,
%U 355687428096017,2425220588831040018,121645100408832019,1364553980880330240020,18677216386213152768021,1152100749379237026969622
%N a(n) = n! * Sum_{d|n} d^(n/d) / d!.
%H Seiichi Manyama, <a href="/A327579/b327579.txt">Table of n, a(n) for n = 1..425</a>
%F E.g.f.: Sum_{k>=1} x^k / ((k - 1)! * (1 - k * x^k)).
%t a[n_] := n! Sum[d^(n/d)/d!, {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]
%t nmax = 22; CoefficientList[Series[Sum[x^k/((k - 1)! (1 - k x^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%o (PARI) a(n) = n! * sumdiv(n, d, d^(n/d) / d!); \\ _Michel Marcus_, Sep 17 2019
%Y Cf. A055225, A057625, A327578, A354843.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Sep 17 2019
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