OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
Expansion of Product_{k>0} (eta(q^k)^4*eta(q^(4*k))^2) / eta(q^(2*k))^6.
a(n) ~ (-1)^n * exp(Pi*sqrt(log(2)*n)) * (log(2))^(1/4) / (4*n^(3/4)). - Vaclav Kotesovec, Oct 26 2018
MATHEMATICA
With[{nmax=80}, CoefficientList[Series[Product[EllipticTheta[4, 0, q^k]/EllipticTheta[3, 0, q^k], {k, 1, nmax+2}], {q, 0, nmax}], q]] (* G. C. Greubel, Oct 29 2018 *)
PROG
(PARI) m=80; q='q+O('q^m); Vec(1/prod(k=1, m+2, eta(q^(2*k))^6/( eta(q^k)^4* eta(q^(4*k))^2) )) \\ G. C. Greubel, Oct 29 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 25 2018
STATUS
approved