OFFSET
0
COMMENTS
In general, if m > 0 and g.f. = Product_{k>=1} (1 + x^((2*k-1)^m)), then a(n) ~ exp((m+1) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m) / m^2)^(m/(m+1)) * n^(1/(m+1)) / 2) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m))^(m/(2*(m+1))) / (2*sqrt(Pi*(m+1)) * m^((m-1)/(2*(m+1))) * n^((2*m+1)/(2*(m+1)))).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..100000
Vaclav Kotesovec, Graph - The asymptotic ratio
FORMULA
G.f.: Product_{k>=1} (1 + x^((2*k-1)^3)).
a(n) ~ exp(2 * 3^(-3/2) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4)) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/8) / (4*3^(1/4) * sqrt(Pi) * n^(7/8)).
MATHEMATICA
nmax = 200; CoefficientList[Series[Product[1 + x^((2*k-1)^3), {k, 1, Floor[nmax^(1/3)/2] + 1}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 18 2017
STATUS
approved