A320069 Expansion of 1/(theta_3(q) * theta_3(q^2)), where theta_3() is the Jacobi theta function.

1, -2, 2, -4, 10, -16, 20, -32, 58, -86, 112, -164, 260, -368, 480, -672, 986, -1348, 1750, -2372, 3312, -4416, 5684, -7520, 10148, -13266, 16912, -21960, 28896, -37168, 46944, -60032, 77466, -98312, 123076, -155392, 197422, -247696, 307540, -384096, 481776, -598500

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

Convolution inverse of A033715.

a(n) ~ (-1)^n * exp(Pi*sqrt(n)) / (8 * n^(5/4)). - Vaclav Kotesovec, Oct 05 2018

Mathematica

CoefficientList[Series[1/Product[EllipticTheta[3, 0, q^k], {k, 1, 2}], {q, 0, 80}], q] (* G. C. Greubel, Oct 29 2018 *)

Prog

(PARI) q='q+O('q^80); Vec(1/prod(k=1, 2, eta(q^(2*k))^5/(eta(q^k)* eta(q^(4*k)))^2 )) \\ G. C. Greubel, Oct 29 2018

Crossrefs

Cf. A000122, A033715, A320068.

Sequence in context: A052175 A102623 A216695 * A002082 A005304 A152732

Adjacent sequences: A320066 A320067 A320068 * A320070 A320071 A320072

Keyword

sign

Author

Seiichi Manyama, Oct 05 2018

Status

approved