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