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%I #5 Jul 22 2020 10:28:48
%S 0,1,1,53,65656,4306202624,21250781850448256,
%T 11198392471992778644752768,847058443993661249394101877997568000,
%U 11916672812223274564264480372420932763474540363776,39215070895580530235582705162664184972620228444352744200981184512
%N a(n) = (n!)^n * [x^n] -log(1 + Sum_{k>=1} (-x)^k / k^n).
%t Table[(n!)^n SeriesCoefficient[-Log[1 + Sum[(-x)^k/k^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]
%t b[n_, k_] := If[n == 0, 0, (-1)^(n + 1) ((n - 1)!)^k - (1/n) Sum[(-1)^(n - j) (Binomial[n, j] (n - j - 1)!)^k j b[j, k], {j, 1, n - 1}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]
%Y Cf. A089064, A336437, A336438, A336439.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Jul 21 2020
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