A061686 Generalized Bell numbers: column 5 of A275043.

1, 1, 17, 1540, 461105, 350813126, 573843627152, 1797582928354025, 9904754169831094065, 89944005095677792967482, 1278494002506675052860358142, 27281796399886236251265603339575, 844252087185585895268923657508727440, 36800471170748991972750857754287551544147

Offset: 0

Author

N. J. A. Sloane, Jun 18 2001

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• 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

Column k=5 of A275043.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n, k)^5*(n-k)*a(k)/n, k=0..n-1))
    end:
seq(a(n), n=0..15); # Alois P. Heinz, Nov 07 2008

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n, k]^5*(n-k)*a[k]/n, {k, 0, n-1}]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 24 2014, after Alois P. Heinz *)

PARI

a61686=[1];A061686(n)={n>1||return(1);#a61686A061686(k))/n} \\ M. F. Hasler, May 11 2015

Formula

Sum_{n>=0} a(n) * x^n / (n!)^5 = exp(Sum_{n>=1} x^n / (n!)^5). - Ilya Gutkovskiy, Jul 17 2020

Extensions

More terms from Alois P. Heinz, Nov 07 2008