A336437 a(n) = (n!)^n * [x^n] -log(1 - Sum_{k>=1} x^k / (k!)^n).

0, 1, 3, 100, 104585, 5781843126, 25450069471437282, 12456703705462747095073458, 900677059707267544414220026068619393, 12337778954350678368447638232258657486399628887370, 39982077640755835496555968029419604779794754953051698069276656138

Offset: 0

Author

Ilya Gutkovskiy, Jul 21 2020

Keywords

• nonn

Crossrefs

Cf. A000629, A102223, A326321, A336427, A336438, 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, 1 + (1/n) Sum[Binomial[n, j]^k j b[j, k], {j, 1, n - 1}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]