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A335811
E.g.f.: exp(x) * Product_{k>=1} (1 + (1 - exp(x))^k).
1
1, 0, 0, -6, -36, -270, -1620, -8526, -41076, -549870, -13520340, -262959246, -3587233716, -22581847470, 584571618540, 30096769542834, 859315925548044, 18434866643574930, 285138881159407020, 2045091797042889714, -28367019385288799796, 379914681728984325330
OFFSET
0,4
COMMENTS
Stirling-Bernoulli transform of A000009.
FORMULA
a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n+1,k+1) * k! * A000009(k).
MATHEMATICA
nmax = 21; CoefficientList[Series[Exp[x] Product[(1 + (1 - Exp[x])^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k StirlingS2[n + 1, k + 1] k! PartitionsQ[k], {k, 0, n}], {n, 0, 21}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 25 2020
STATUS
approved