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%I #7 Aug 12 2020 11:10:27
%S 1,8,45,544,3725,89856,858823,25271296,434776329,13241728000,
%T 285750755411,11494661861376,302956057862653,12945137688641536,
%U 446924199188379375,20735627677666902016,827246308572614396177,43155924331583693389824
%N a(n) = n! * Sum_{d|n} n^d / d!.
%F a(n) = n! * [x^n] Sum_{k>=1} (exp(n*x^k) - 1).
%t Table[n! Sum[n^d/d!, {d, Divisors[n]}], {n, 1, 18}]
%t Table[n! SeriesCoefficient[Sum[(Exp[n x^k] - 1), {k, 1, n}], {x, 0, n}], {n, 1, 18}]
%o (PARI) a(n) = n! * sumdiv(n, d, n^d/d!); \\ _Michel Marcus_, Aug 12 2020
%Y Cf. A057625, A063170, A066108.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Aug 10 2020
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