A320967 Expansion of Product_{k>0} theta_3(q^k)/theta_4(q^k), where theta_3() and theta_4() are the Jacobi theta functions.

1, 4, 12, 36, 92, 220, 508, 1108, 2332, 4776, 9492, 18420, 35036, 65324, 119708, 216044, 384204, 674236, 1168968, 2003460, 3397300, 5704148, 9487740, 15642676, 25577900, 41495032, 66817812, 106837112, 169677372, 267755836, 419948980, 654799316, 1015276412, 1565765892

Offset: 0

Author

Seiichi Manyama, Oct 25 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Crossrefs

Self-convolution of A320968.

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

Programs

Mathematica

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 *)

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

Formula

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