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%I #7 Jul 22 2020 10:28:42
%S 0,1,1,46,63111,4226436876,21095962423437280,
%T 11165885881625823212655540,846105231095934499366980692096995455,
%U 11911559696594230804398683820096471009503594129080,39208751872375132639833577214095359308827747721266594509276656136
%N a(n) = (n!)^n * [x^n] -log(Sum_{k>=0} (-x)^k / (k!)^n).
%t Table[(n!)^n SeriesCoefficient[-Log[Sum[(-x)^k/(k!)^n, {k, 0, n}]], {x, 0, n}], {n, 0, 10}]
%t b[n_, k_] := If[n == 0, 0, (-1)^(n + 1) - (1/n) Sum[(-1)^(n - j) Binomial[n, j]^k j b[j, k], {j, 1, n - 1}]];a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]
%Y Cf. A002190, A193420, A275044, A336437, A336438, A336440.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Jul 21 2020
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