OFFSET
0,2
COMMENTS
In general, if a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} (1 + x^(a*k+b))/(1 - x^(a*k+b)), then a(n) ~ Gamma(b/a) * a^(b/(2*a) - 1/2) * Pi^(b/a - 1) * exp(Pi*sqrt(n/a)) / (2^(2*b/a + 1) * n^(b/(2*a) + 1/2)).
FORMULA
a(n) ~ exp(Pi*sqrt(n)/2) * Gamma(1/4) / (2^(9/4) * Pi^(3/4) * n^(5/8)).
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[(1 + x^(4*k+1))/(1 - x^(4*k+1)), {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 26 2015
STATUS
approved