OFFSET
0,2
COMMENTS
In general, if j > 0, a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} 1/(1 - x^(a*k+b))^j, then a(n) ~ Gamma(b/a)^j * 2^(-(j+5)/4 - j*b/(2*a)) * 3^((j-1)/4 - j*b/(2*a)) * j^(-(j-1)/4 + j*b/(2*a)) * a^(-(j+1)/4 + j*b/(2*a)) * Pi^(-j + j*b/a) * n^((j-3)/4 - j*b/(2*a)) * exp(Pi*sqrt(2*j*n/(3*a))).
FORMULA
a(n) ~ exp(Pi*sqrt(2*n/3)) * 6^(1/4) * Gamma(1/4)^4 / (32 * Pi^3 * n^(1/4)).
MATHEMATICA
nmax=50; CoefficientList[Series[Product[1/(1-x^(4*k+1))^4, {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 27 2015
STATUS
approved