A317274 a(n) = Sum_{k=0..n} binomial(n,k)*Stirling1(n,k).

1, 1, -1, -2, 19, -79, 76, 2640, -36945, 329371, -1861949, -4438774, 355714228, -7292531180, 109844527612, -1277006731104, 8181112825231, 124379387459175, -6806984421310187, 191750786928500050, -4289244423048443149, 80163499107525756105, -1146313133241947091420, 5494990440819210736560

Offset: 0

Author

Ilya Gutkovskiy, Jul 25 2018

Keywords

• sign

Comments

Binomial convolution of the signed Stirling numbers of the first kind.

Crossrefs

Cf. A008275, A048994, A122455, A211210, A211211.

Programs

Mathematica

Table[Sum[Binomial[n, k] StirlingS1[n, k], {k, 0, n}], {n, 0, 23}]

PARI

a(n) = sum(k=0, n, binomial(n, k)*stirling(n, k, 1)); \\ Michel Marcus, Aug 07 2019