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A061686 Generalized Bell numbers. 3
1, 1, 17, 1540, 461105, 350813126, 573843627152, 1797582928354025, 9904754169831094065, 89944005095677792967482, 1278494002506675052860358142, 27281796399886236251265603339575, 844252087185585895268923657508727440, 36800471170748991972750857754287551544147 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

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-Fran├žois Alcover, Mar 24 2014, after Alois P. Heinz *)

PROG

(PARI) a61686=[1]; A061686(n)={n>1||return(1); #a61686<n&&a61686=concat(a61686, vector(n-#a61686)); a61686[n]&&return(a61686[n]); a61686[n]=sum(k=0, n-1, binomial(n, k)^5*(n-k)*A061686(k))/n} \\ M. F. Hasler, May 11 2015

CROSSREFS

Column k=5 of A275043.

Sequence in context: A242282 A129911 A104808 * A133590 A227887 A144571

Adjacent sequences:  A061683 A061684 A061685 * A061687 A061688 A061689

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 18 2001

EXTENSIONS

More terms from Alois P. Heinz, Nov 07 2008

STATUS

approved

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Last modified June 6 10:30 EDT 2020. Contains 334846 sequences. (Running on oeis4.)