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A292916
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a(n) = n! * [x^n] exp(n*x)/(2 - exp(x)).
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4
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1, 2, 11, 94, 1083, 15666, 272451, 5532206, 128409707, 3352959850, 97259891163, 3102552150006, 107936130271899, 4066743353318114, 164961642651034547, 7167348523420169278, 332081754670735087275, 16343667009638859878298, 851478575825591156040843, 46814697307371602567813126
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OFFSET
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0,2
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COMMENTS
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The n-th term of the n-th binomial transform of A000670.
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, k) option remember; k^n +add(
binomial(n, j)*b(j, k), j=0..n-1)
end:
a:= n-> b(n$2):
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MATHEMATICA
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Table[n! SeriesCoefficient[Exp[n x]/(2 - Exp[x]), {x, 0, n}], {n, 0, 19}]
Table[HurwitzLerchPhi[1/2, -n, n]/2, {n, 0, 19}]
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PROG
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(PARI) a000670(n) = sum(k=0, n, k!*stirling(n, k, 2));
a(n) = 2^n*a000670(n)-sum(k=0, n-1, 2^k*(n-1-k)^n); \\ Seiichi Manyama, Dec 25 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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