A336831 a(n) = (n!)^n * [x^n] exp(-Sum_{k>=1} (-x)^k / (k!)^n).

1, 1, 1, 10, 4359, 91406876, 111657668637280, 11436881770074767723291, 137560155520600195617494951186559, 260122627893213770028102613184254361777327032, 99781796293430843492956500115058179262448159117567276656136

Offset: 0

Author

Ilya Gutkovskiy, Aug 05 2020

Keywords

• nonn

Crossrefs

Cf. A000587, A275044, A336209, A336210, A336439.

Programs

Mathematica

Table[(n!)^n SeriesCoefficient[Exp[-Sum[(-x)^k/(k!)^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]
b[n_, k_] := b[n, k] = If[n == 0, 1, -Sum[(-1)^(n - j) Binomial[n, j]^k (n - j) b[j, k], {j, 0, n - 1}]/n]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]