OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
a(n) = (-1)^n * A320078(n).
Expansion of Product_{k>0} (eta(q^k)^2*eta(q^(4*k))) / eta(q^(2*k))^3.
Expansion of Product_{k>0} theta_4(q^(2*k-1)).
a(n) ~ (-1)^n * (log(2))^(1/4) * exp(Pi*sqrt(n*log(2)/2)) / (4*n^(3/4)). - Vaclav Kotesovec, Oct 26 2018
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[Sqrt[EllipticTheta[4, 0, x^k] / EllipticTheta[3, 0, x^k]], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 26 2018 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 26 2018
STATUS
approved