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Expansion of 1/(theta_3(q) * theta_3(q^2) * theta_3(q^3)), where theta_3() is the Jacobi theta function.
2

%I #15 Oct 30 2018 03:35:50

%S 1,-2,2,-6,14,-20,32,-60,98,-150,232,-360,558,-828,1196,-1776,2614,

%T -3700,5238,-7480,10516,-14592,20180,-27832,38216,-51970,70184,-94842,

%U 127612,-170140,226164,-300324,396754,-521520,683484,-893432,1164330,-1511188,1954756,-2524188

%N Expansion of 1/(theta_3(q) * theta_3(q^2) * theta_3(q^3)), where theta_3() is the Jacobi theta function.

%H Seiichi Manyama, <a href="/A320070/b320070.txt">Table of n, a(n) for n = 0..10000</a>

%F Convolution inverse of A029594.

%F a(n) ~ (-1)^n * exp(2*Pi*sqrt(n/3)) / (4*sqrt(6)*n^(3/2)). - _Vaclav Kotesovec_, Oct 05 2018

%t CoefficientList[Series[1/Product[EllipticTheta[3, 0, q^k], {k, 1, 3}], {q, 0, 80}], q] (* _G. C. Greubel_, Oct 29 2018 *)

%o (PARI) q='q+O('q^80); Vec(1/prod(k=1,3, eta(q^(2*k))^5/(eta(q^k)* eta(q^(4*k)))^2 )) \\ _G. C. Greubel_, Oct 29 2018

%Y Cf. A000122, A029594, A320068.

%K sign

%O 0,2

%A _Seiichi Manyama_, Oct 05 2018