login
Expansion of Product_{k>0} theta_3(q^k)/theta_4(q^k), where theta_3() and theta_4() are the Jacobi theta functions.
4

%I #26 Oct 30 2018 05:43:23

%S 1,4,12,36,92,220,508,1108,2332,4776,9492,18420,35036,65324,119708,

%T 216044,384204,674236,1168968,2003460,3397300,5704148,9487740,

%U 15642676,25577900,41495032,66817812,106837112,169677372,267755836,419948980,654799316,1015276412,1565765892

%N Expansion of Product_{k>0} theta_3(q^k)/theta_4(q^k), where theta_3() and theta_4() are the Jacobi theta functions.

%H Vaclav Kotesovec, <a href="/A320967/b320967.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>

%F Expansion of Product_{k>0} eta(q^(2*k))^6 / (eta(q^k)^4*eta(q^(4*k))^2).

%t With[{nmax=50}, CoefficientList[Series[Product[EllipticTheta[3, 0, q^k]/EllipticTheta[4, 0, q^k], {k, 1, nmax+2}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Oct 29 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(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

%Y Self-convolution of A320968.

%Y Cf. A000122, A002448, A007096, A301554, A320067, A320970.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 25 2018