OFFSET
0,4
COMMENTS
In general, if m > 1 and g.f. = Sum_{k>=0} q(k)^m * x^k / Sum_{k>=0} q(k)*x^k, then a(n, m) ~ exp(Pi*sqrt((m^2 - 1)*n/3)) * (m^2 - 1)^(3*m/4 - 1/2) / (2^(2*m - 1/2) * 3^(m/4) * m^(3*m/2 - 1) * n^(3*m/4)).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (81*6^(1/4)*n^(9/4)).
MATHEMATICA
nmax = 50; CoefficientList[Series[Sum[PartitionsQ[k]^3*x^k, {k, 0, nmax}] / Sum[PartitionsQ[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 20 2018
STATUS
approved