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A335812
E.g.f.: Product_{k>=1} 1 / (1 - (1 - exp(x))^k).
3
1, -1, 3, -7, 39, -31, 1623, 9953, 182199, 2116289, 32269143, 505278113, 9743069559, 214428606209, 5156280298263, 127321200213473, 3176128419544119, 80737907621585729, 2147513299611040983, 61423058495936864033, 1912348969322283717879, 64216042408215934910849
OFFSET
0,3
COMMENTS
Inverse binomial transform of A327601.
FORMULA
a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n,k) * k! * A000041(k).
MATHEMATICA
nmax = 21; CoefficientList[Series[ Product[1/(1 - (1 - Exp[x])^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k StirlingS2[n, k] k! PartitionsP[k], {k, 0, n}], {n, 0, 21}]
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k * stirling(n, k, 2) * k! * numbpart(k)); \\ Michel Marcus, Jun 25 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 25 2020
STATUS
approved