OFFSET
0,8
COMMENTS
Convolution inverse of A270995.
LINKS
Eric Weisstein's World of Mathematics, Partition Function Q
FORMULA
G.f.: Product_{k>=1} (1 - A000009(k)*x^k).
MATHEMATICA
nmax = 51; CoefficientList[Series[Product[(1 - PartitionsQ[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[-Sum[d PartitionsQ[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 51}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 18 2018
STATUS
approved