OFFSET
0,2
COMMENTS
In general, if m > 0 and g.f. = Product_{k>=1} (1 + x^(k^m)) / (1 - x^(k^m)), then a(n) ~ exp((m+1) * ((2^(1 + 1/m) - 1) * Gamma(1/m) * Zeta(1 + 1/m) / m^2)^(m/(m+1)) * (n/2)^(1/(m+1))) * ((2^(1 + 1/m) - 1) * Gamma(1/m) * Zeta(1 + 1/m))^(m/(m+1)) / (sqrt(m+1) * 2^(m/2 + (m+2)/(m+1)) * m^((3*m-1)/(2*(m+1))) * Pi^((m+1)/2) * n^((3*m+1)/(2*(m+1)))).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(2^(7/4) * ((2^(4/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4) / 3^(3/2)) * ((2^(4/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/4) / (3 * 2^(15/4) * Pi^2 * n^(5/4)).
MATHEMATICA
nmax=150; CoefficientList[Series[Product[(1+x^(k^3))/(1-x^(k^3)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 30 2016
STATUS
approved