A061694 Generalized Bell numbers.

0, 0, 36, 864, 17500, 351000, 7197169, 151633440, 3275925804, 72315234000, 1625547144199, 37102497859152, 857909644412275, 20059247889751161, 473562712831103536, 11274693857547716640, 270435401233629732940

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Vaclav Kotesovec, Recurrence (of order 6)

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) = 1/6*Sum_{i+j+k=n, i, j, k>0} (n!/(i!*j!*k!))^3. - Vladeta Jovovic, Apr 23 2003

a(n) ~ 3^(3*n+1) / (8*Pi^2*n^2). - Vaclav Kotesovec, Mar 14 2014

Sum_{n>=1} a(n) * x^n / (n!)^3 = (1/6) * ( Sum_{n>=1} x^n / (n!)^3 )^3. - Ilya Gutkovskiy, Mar 04 2021

Mathematica

Table[Sum[Sum[(n!/(i!*j!*(n-i-j)!))^3/6, {i, 1, n-j-1}], {j, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 14 2014 *)

Crossrefs

Sequence in context: A004360 A238931 A081142 * A264192 A122038 A222926

Adjacent sequences: A061691 A061692 A061693 * A061695 A061696 A061697

Keyword

nonn

Author

N. J. A. Sloane, Jun 19 2001

Extensions

More terms from Vladeta Jovovic, Apr 23 2003

Status

approved