A061695 Generalized Bell numbers.

1, 27, 864, 36000, 1944000, 133358400, 11379916800, 1185137049600, 148142131200000, 21908575180800000, 3785801791242240000, 756127866850836480000, 172901238886557941760000, 44887821634010234880000000, 13132894100921851576320000000, 4301460581188603786297344000000

Offset: 1

Author

N. J. A. Sloane, Jun 19 2001

Keywords

• nonn

Links

• J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

Crossrefs

First subdiagonal of A061692.

Programs

Mathematica

Table[((n+1)!)^2 (n+1) n/8,{n,20}] (* Harvey P. Dale, Jul 25 2024 *)

Formula

a(n) = (n+1)!^2*(n+1)n/8 = A162993(n)*A000217(n). - Oleksandr Kulkov, Oct 10 2022

D-finite with recurrence (-n+1)*a(n) +(n+1)^3*a(n-1)=0. - R. J. Mathar, Jan 17 2025

Extensions

a(8)-a(16) from Alois P. Heinz, Sep 10 2019