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A061687
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Generalized Bell numbers.
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3
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1, 1, 33, 8506, 9483041, 33056715626, 293327384637282, 5747475089121405893, 224054040415856117594913, 16044797009828490454609378642, 1981736776623437001042672440089658, 401147408702290404750740714717055504773, 127573929384655691416638350563783440408133922
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..117
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.
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FORMULA
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Sum_{n>=0} a(n) * x^n / (n!)^6 = exp(Sum_{n>=1} x^n / (n!)^6). - 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)^6*(n-k)*a(k)/n, k=0..n-1))
end:
seq(a(n), n=0..15); # Alois P. Heinz, Nov 07 2008
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MATHEMATICA
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a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n, k]^6*(n-k)*a[k]/n, {k, 0, n-1}]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)
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CROSSREFS
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Column k=6 of A275043.
Sequence in context: A336197 A336261 A060705 * A116056 A337807 A232148
Adjacent sequences: A061684 A061685 A061686 * A061688 A061689 A061690
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jun 18 2001
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EXTENSIONS
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More terms from Alois P. Heinz, Nov 07 2008
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STATUS
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approved
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