A211210 a(n) = Sum_{k=0..n} binomial(n, k)*|S1(n, k)|.

1, 1, 3, 16, 115, 1021, 10696, 128472, 1734447, 25937683, 424852351, 7554471156, 144767131444, 2971727661124, 65013102375404, 1509186299410896, 37032678328740751, 957376811266995031, 25999194631060525009, 739741591417352081464, 22000132609456951524051

Offset: 0

Author

Olivier Gérard, Oct 23 2012

Keywords

• nonn

Comments

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

Row sums of triangle A187555.

Crossrefs

Cf. A317274 (signed S1), A187555, A134090, A211211.

Cf. A122455 (second kind), A271702, A134094, A343841 (second kind inverse).

Programs

Mathematica

Table[Sum[Binomial[n, k] Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 20}]

PARI

a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(n, k, 1))); \\ Michel Marcus, May 10 2021