A029843 Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^6.

1, 6, 9, -10, -24, 36, 65, -102, -153, 232, 327, -468, -663, 918, 1287, -1768, -2391, 3240, 4289, -5676, -7488, 9758, 12753, -16524, -21250, 27300, 34758, -44128, -55896, 70380, 88519, -110874, -138285, 172136, 213315

Offset

0,2

Links

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

Formula

G.f.: x^(3/4)*theta_2(sqrt(x))^6/theta_2(x)^6, where theta_() is the Jacobi theta function. - Ilya Gutkovskiy, Dec 04 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = 8 * exp(-3*Pi/4) * 2^(3/4) = A388382. - Simon Plouffe, Sep 15 2025

Crossrefs

Cf. A029838, A029839, A029840, A029841, A029842, A029844.

Sequence in context: A130593 A328234 A051221 * A209941 A000729 A280666

Adjacent sequences: A029840 A029841 A029842 * A029844 A029845 A029846

Keyword

sign

Author

N. J. A. Sloane

Status

approved