A336949 a(n) = n! * [x^n] 1 / (exp(-n*x) - x).

1, 2, 14, 195, 4440, 147745, 6698448, 394852577, 29250137472, 2652483234033, 288363456748800, 36952298766628465, 5504130616452258816, 941845623036360908489, 183298110723156455921664, 40221612394630225987208625, 9876429434585097671993032704

Offset: 0

Author

Ilya Gutkovskiy, Aug 08 2020

Keywords

• nonn

Crossrefs

Cf. A063170, A072597, A235328, A336947, A336948.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(Exp[-n x] - x), {x, 0, n}], {n, 0, 16}]
Join[{1}, Table[n! Sum[(n (n - k + 1))^k/k!, {k, 0, n}], {n, 1, 16}]]

PARI

a(n)={n!*polcoef(1/(exp(-n*x + O(x*x^n)) - x), n)} \\ Andrew Howroyd, Aug 08 2020

Formula

a(n) = n! * Sum_{k=0..n} (n * (n-k+1))^k / k!.