A336439 a(n) = (n!)^n * [x^n] -log(Sum_{k>=0} (-x)^k / (k!)^n).

0, 1, 1, 46, 63111, 4226436876, 21095962423437280, 11165885881625823212655540, 846105231095934499366980692096995455, 11911559696594230804398683820096471009503594129080, 39208751872375132639833577214095359308827747721266594509276656136

Offset: 0

Author

Ilya Gutkovskiy, Jul 21 2020

Keywords

• nonn

Crossrefs

Cf. A002190, A193420, A275044, A336437, A336438, A336440.

Programs

Mathematica

Table[(n!)^n SeriesCoefficient[-Log[Sum[(-x)^k/(k!)^n, {k, 0, n}]], {x, 0, n}], {n, 0, 10}]
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}]