A061693 Generalized Bell numbers.

0, 4, 27, 172, 1125, 7591, 52479, 369580, 2640465, 19082629, 139207959, 1023462199, 7574172879, 56369211679, 421563478527, 3166149812140, 23868662788809, 180538738842217, 1369635435497367, 10418413517675797

Offset

1,2

Links

Table of n, a(n) for n=1..20.

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.

Formula

a(n) = A000172(n)/2-1. - Vladeta Jovovic, Apr 23 2003

Sum_{n>=1} a(n) * x^n / (n!)^3 = (1/2) * ( Sum_{n>=1} x^n / (n!)^3 )^2. - Ilya Gutkovskiy, Mar 04 2021

Mathematica

a[n_] := Sum[Binomial[n, k]^3, {k, 0, n}]/2 - 1;
a[n_] := n^2*HypergeometricPFQ[{1 - n, 1 - n, 1 - n}, {2, 2}, -1] - 1;
Table[a[n], {n, 1, 20}] (* Peter Luschny, Apr 17 2022 *)

Crossrefs

Sequence in context: A015534 A306054 A218274 * A005974 A289718 A010910

Adjacent sequences: A061690 A061691 A061692 * A061694 A061695 A061696

Keyword

nonn

Author

N. J. A. Sloane, Jun 19 2001

Status

approved