A336440 a(n) = (n!)^n * [x^n] -log(1 + Sum_{k>=1} (-x)^k / k^n).

0, 1, 1, 53, 65656, 4306202624, 21250781850448256, 11198392471992778644752768, 847058443993661249394101877997568000, 11916672812223274564264480372420932763474540363776, 39215070895580530235582705162664184972620228444352744200981184512

Offset: 0

Author

Ilya Gutkovskiy, Jul 21 2020

Keywords

• nonn

Crossrefs

Cf. A089064, A336437, A336438, A336439.

Programs

Mathematica

Table[(n!)^n SeriesCoefficient[-Log[1 + Sum[(-x)^k/k^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]
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}]