A321027 Expansion of Product_{k>0} theta_3(q^(2*k))/theta_3(q^(2*k-1)), where theta_3() is the Jacobi theta function.
1, -2, 6, -14, 28, -58, 114, -210, 384, -684, 1178, -2010, 3372, -5538, 9006, -14466, 22906, -35954, 55884, -85946, 131176, -198622, 298274, -444958, 659368, -970544, 1420362, -2066876, 2990680, -4305598, 6168154, -8793554, 12480718, -17637250, 24818530, -34785622
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)
- Eric Weisstein's World of Mathematics, Jacobi Theta Functions
Programs
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Mathematica
nmax = 50; CoefficientList[Series[Product[EllipticTheta[3, 0, x^(2*k)] / EllipticTheta[3, 0, x^(2*k-1)], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 26 2018 *)