A343579 a(n) = Sum_{k=0..floor(n/2)} |Stirling1(n - k, k)|.

1, 0, 1, 1, 3, 9, 36, 176, 1030, 7039, 55098, 486346, 4780445, 51787405, 613045468, 7873065045, 109021348618, 1619197654575, 25675094145535, 432908683794379, 7733991639921585, 145933532935469016, 2900112108790279902, 60543749629794205640, 1324677739541613767983

Offset

0,5

Comments

Equals antidiagonal sums of the triangle of unsigned Stirling numbers of the first kind (A132393).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..451

Formula

a(n) ~ n! / n^2. - Vaclav Kotesovec, Apr 09 2022

Mathematica

Table[Sum[Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Vaclav Kotesovec, Apr 09 2022 *)

Prog

(PARI) a(n) = sum(k=0, n\2, abs(stirling(n-k, k, 1))); \\ Michel Marcus, Apr 22 2021
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, j+x))) \\ Seiichi Manyama, Apr 08 2022

Crossrefs

Cf. A132393, A320963.

Variant: A237653.

Keyword

nonn

Author

Peter Luschny, Apr 20 2021

Status

approved