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A061688
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Generalized Bell numbers.
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3
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1, 1, 65, 48844, 209175233, 3464129078126, 173566857025139312, 22208366234650578141209, 6409515697874502425444186817, 3794729706423816704068204814925754, 4276126299841623727960390049367617509190, 8631647765438316626054238101611711249984175399
(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!)^7 = exp(Sum_{n>=1} x^n / (n!)^7). - 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)^7*(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]^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 *)
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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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