A336969 a(n) = n! * [x^n] 1 / (exp(n*x) - x).

1, 0, -2, 33, -424, 495, 342864, -22382913, 915074432, -913039857, -5455432211200, 812138028148623, -75257247474017280, 1984517460320303415, 1155562494647499610112, -361521639388178369672625, 67461150715150454861692928, -6658374003334822571921759457

Offset: 0

Author

Ilya Gutkovskiy, Aug 09 2020

Keywords

• sign

Crossrefs

Cf. A089148, A134095, A302398, A336949, A336958.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(Exp[n x] - x), {x, 0, n}], {n, 0, 17}]
Join[{1}, Table[n! Sum[(-n (n - k + 1))^k/k!, {k, 0, n}], {n, 1, 17}]]

Formula

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