A383839 a(n) = [x^n] 1/(1 - n*x) * Product_{k=0..n-1} (1 + k*x)/(1 - k*x).

1, 1, 10, 177, 4576, 156145, 6627006, 336562177, 19906794496, 1344082891761, 102012257669950, 8597688151223281, 796733925564191616, 80516951813773009249, 8812696026991760928766, 1038540275078155878285825, 131107274213106172807069696, 17652158052761888943436783009

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * Stirling2(k+n,n).

Prog

(PARI) a(n) = sum(k=0, n, abs(stirling(n, k, 1))*stirling(k+n, n, 2));

Crossrefs

Cf. A350366, A383767.

Sequence in context: A053537 A049380 A302105 * A200060 A240561 A057122

Adjacent sequences: A383836 A383837 A383838 * A383840 A383841 A383842

Keyword

nonn

Author

Seiichi Manyama, May 14 2025

Status

approved