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

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Formula

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

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 *)

Prog

(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

Crossrefs

Self-convolution of A320968.

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

Sequence in context: A190072 A063810 A183931 * A261584 A347990 A002842

Adjacent sequences: A320964 A320965 A320966 * A320968 A320969 A320970

Keyword

nonn

Author

Seiichi Manyama, Oct 25 2018

Status

approved