OFFSET
0,3
COMMENTS
In general, if m > 1 and g.f. = Product_{k>=1} ((1-x^(m*k))/(1-x^k))^k, then a(n, m) ~ exp(3 * 2^(-2/3) * ((1-1/m^2)*Zeta(3))^(1/3) * n^(2/3)) * ((1-1/m^2)*Zeta(3))^(1/6) / (2^(1/3) * sqrt(3*Pi) * m^(1/12) * n^(2/3)).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ exp(2^(1/3) * 3^(4/3) * 5^(-2/3) * Zeta(3)^(1/3) * n^(2/3)) * (2*Zeta(3))^(1/6) / (3^(1/3) * 5^(5/12) * sqrt(Pi) * n^(2/3)).
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[((1-x^(5*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 15 2017
STATUS
approved