%I #5 Jul 22 2020 10:28:54
%S 1,1,3,71,30232,435772624,357189846148256,25740403176657987904960,
%T 234446578865185870182814945640448,
%U 363178754511398964104990417951192651478859776,122088173887703514886799765831338556792096849201928981184512
%N a(n) = (n!)^n * [x^n] exp(Sum_{k>=1} x^k / k^n).
%t Table[(n!)^n SeriesCoefficient[Exp[Sum[x^k/k^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]
%t b[n_, k_] := If[n == 0, 1, (1/n) Sum[(Binomial[n, j] (n - j - 1)!)^k (n - j) b[j, k], {j, 0, n - 1}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]
%Y Cf. A000142, A074707, A193436, A217145, A275044.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 21 2020
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