A061688 Generalized Bell numbers: column 7 of A275043.

1, 1, 65, 48844, 209175233, 3464129078126, 173566857025139312, 22208366234650578141209, 6409515697874502425444186817, 3794729706423816704068204814925754, 4276126299841623727960390049367617509190, 8631647765438316626054238101611711249984175399

Offset: 0

Author

N. J. A. Sloane, Jun 18 2001

Keywords

• nonn

Links

• Alois P. Heinz, 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=7 of A275043.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n, k)^7*(n-k)*a(k)/n, k=0..n-1))
    end:
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 07 2008

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n, k]^7*(n-k)*a[k]/n, {k, 0, n-1}]]; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Apr 17 2014, after Alois P. Heinz *)

Formula

Sum_{n>=0} a(n) * x^n / (n!)^7 = exp(Sum_{n>=1} x^n / (n!)^7). - Ilya Gutkovskiy, Jul 17 2020

Extensions

More terms from Alois P. Heinz, Nov 07 2008