A320968 Expansion of (Product_{k>0} theta_3(q^k)/theta_4(q^k))^(1/2), where theta_3() and theta_4() are the Jacobi theta functions.

1, 2, 4, 10, 18, 34, 64, 110, 188, 320, 524, 846, 1358, 2130, 3308, 5102, 7750, 11674, 17468, 25862, 38022, 55558, 80532, 116034, 166284, 236784, 335416, 472868, 663146, 925762, 1286920, 1780962, 2454792, 3370806, 4610656, 6284090, 8535868, 11554834, 15591564

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

a(n) = (-1)^n * A320098(n).

Expansion of Product_{k>0} eta(q^(2*k))^3 / (eta(q^k)^2*eta(q^(4*k))).

Expansion of Product_{k>0} 1/theta_4(q^(2*k-1)).

Mathematica

CoefficientList[Series[1/Product[EllipticTheta[4, 0, q^(2*k - 1)], {k, 1, 50}], {q, 0, 80}], q] (* G. C. Greubel, Oct 29 2018 *)

Prog

(PARI) q='q+O('q^80); Vec(prod(k=1, 50, eta(q^(2*k))^3/(eta(q^k)^2* eta(q^(4*k))) )) \\ G. C. Greubel, Oct 29 2018

Crossrefs

Cf. A000122, A002448, A080054 ((theta_3(q^k)/theta_4(q^k))^(1/2)), A320098, A320967, A320992.

Sequence in context: A093695 A308529 A320098 * A279359 A242261 A189892

Adjacent sequences: A320965 A320966 A320967 * A320969 A320970 A320971

Keyword

nonn

Author

Seiichi Manyama, Oct 25 2018

Status

approved