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A061686 Generalized Bell numbers. 4
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
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
Sum_{n>=0} a(n) * x^n / (n!)^5 = exp(Sum_{n>=1} x^n / (n!)^5). - Ilya Gutkovskiy, Jul 17 2020
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 *)
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: A336196 A336260 A104808 * A133590 A227887 A144571
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 March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)