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A061686
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Generalized Bell numbers.
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4
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1, 1, 17, 1540, 461105, 350813126, 573843627152, 1797582928354025, 9904754169831094065, 89944005095677792967482, 1278494002506675052860358142, 27281796399886236251265603339575, 844252087185585895268923657508727440, 36800471170748991972750857754287551544147
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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Sum_{n>=0} a(n) * x^n / (n!)^5 = exp(Sum_{n>=1} x^n / (n!)^5). - Ilya Gutkovskiy, Jul 17 2020
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n, k)^5*(n-k)*a(k)/n, k=0..n-1))
end:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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