A336438 a(n) = (n!)^n * [x^n] -log(1 - Sum_{k>=1} x^k / k^n).

0, 1, 3, 107, 109720, 5916402624, 25690641168448256, 12501662072725447325457536, 901886074956174349048867091963183104, 12343856662712388173832816538241443833756015132672, 39989244654801819205752864236178211163455535276138236680981184512

Offset: 0

Author

Ilya Gutkovskiy, Jul 21 2020

Keywords

• nonn

Crossrefs

Cf. A003713, A074708, A336436, A336437, A336439, A336440.

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, ((n - 1)!)^k + (1/n) Sum[(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}]