OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Partition Function Q
FORMULA
G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*q(j)^k*x^(j*k)/k).
MATHEMATICA
nmax = 44; CoefficientList[Series[Product[1/(1 + PartitionsQ[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 44; CoefficientList[Series[Exp[Sum[Sum[(-1)^k PartitionsQ[j]^k x^(j k)/k, {j, 1, nmax}], {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, 44}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 27 2018
STATUS
approved