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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.
8
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 25 2018
STATUS
approved