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%I #16 Oct 30 2018 03:35:42
%S 1,-2,2,-4,10,-16,20,-32,58,-86,112,-164,260,-368,480,-672,986,-1348,
%T 1750,-2372,3312,-4416,5684,-7520,10148,-13266,16912,-21960,28896,
%U -37168,46944,-60032,77466,-98312,123076,-155392,197422,-247696,307540,-384096,481776,-598500
%N Expansion of 1/(theta_3(q) * theta_3(q^2)), where theta_3() is the Jacobi theta function.
%H Seiichi Manyama, <a href="/A320069/b320069.txt">Table of n, a(n) for n = 0..10000</a>
%F Convolution inverse of A033715.
%F a(n) ~ (-1)^n * exp(Pi*sqrt(n)) / (8 * n^(5/4)). - _Vaclav Kotesovec_, Oct 05 2018
%t CoefficientList[Series[1/Product[EllipticTheta[3, 0, q^k], {k, 1, 2}], {q, 0, 80}], q] (* _G. C. Greubel_, Oct 29 2018 *)
%o (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
%Y Cf. A000122, A033715, A320068.
%K sign
%O 0,2
%A _Seiichi Manyama_, Oct 05 2018
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