A318616 a(n) = n! * [x^n] (1 - x)^(n*x).

1, 0, -4, -9, 160, 1350, -14904, -335160, 1796096, 125615448, 204300000, -64591072920, -735003528192, 41673388751280, 1113912529707264, -30043364514345000, -1703374149711298560, 17822402097051182400, 2856178489894627203072, 12394040043610922716800, -5255899207995216384000000

Offset: 0

Author

Ilya Gutkovskiy, Aug 30 2018

Keywords

• sign

Crossrefs

Cf. A007114, A008275, A318615.

Programs

Mathematica

Table[n! SeriesCoefficient[(1 - x)^(n x), {x, 0, n}], {n, 0, 20}]
Join[{1}, Table[n! Sum[(-1)^k n^(n - k) StirlingS1[k, n - k]/k!, {k, n}], {n, 20}]]

Formula

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

a(n) = n! * Sum_{k=0..n} (-1)^k*n^(n-k)*Stirling1(k,n-k)/k!.