OFFSET
0,4
COMMENTS
Inverse binomial transform of A335811.
FORMULA
a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n,k) * k! * A000009(k).
MATHEMATICA
nmax = 21; CoefficientList[Series[Product[(1 + (1 - Exp[x])^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k StirlingS2[n, k] k! PartitionsQ[k], {k, 0, n}], {n, 0, 21}]
PROG
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+(1-exp(x))^k))) \\ Seiichi Manyama, Jul 08 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 25 2020
STATUS
approved