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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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 A002842 A051041

Adjacent sequences:  A320964 A320965 A320966 * A320968 A320969 A320970

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 25 2018

STATUS

approved

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Last modified August 5 15:41 EDT 2021. Contains 346477 sequences. (Running on oeis4.)