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A320069
Expansion of 1/(theta_3(q) * theta_3(q^2)), where theta_3() is the Jacobi theta function.
2
1, -2, 2, -4, 10, -16, 20, -32, 58, -86, 112, -164, 260, -368, 480, -672, 986, -1348, 1750, -2372, 3312, -4416, 5684, -7520, 10148, -13266, 16912, -21960, 28896, -37168, 46944, -60032, 77466, -98312, 123076, -155392, 197422, -247696, 307540, -384096, 481776, -598500
OFFSET
0,2
LINKS
FORMULA
Convolution inverse of A033715.
a(n) ~ (-1)^n * exp(Pi*sqrt(n)) / (8 * n^(5/4)). - Vaclav Kotesovec, Oct 05 2018
MATHEMATICA
CoefficientList[Series[1/Product[EllipticTheta[3, 0, q^k], {k, 1, 2}], {q, 0, 80}], q] (* G. C. Greubel, Oct 29 2018 *)
PROG
(PARI) q='q+O('q^80); Vec(1/prod(k=1, 2, eta(q^(2*k))^5/(eta(q^k)* eta(q^(4*k)))^2 )) \\ G. C. Greubel, Oct 29 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 05 2018
STATUS
approved