A029844 Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^7.

1, 7, 14, -7, -42, 28, 133, -90, -357, 231, 833, -511, -1792, 1064, 3695, -2163, -7329, 4221, 13923, -7847, -25536, 14161, 45703, -25109, -80010, 43526, 136941, -73654, -229823, 122493, 379582, -200935, -617729, 324751

Offset

0,2

Links

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

Formula

G.f.: x^(7/8)*theta_2(sqrt(x))^7/theta_2(x)^7, where theta_() is the Jacobi theta function. - Ilya Gutkovskiy, Dec 04 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = 16 * exp(-7*Pi/8) * 2^(3/8) = A388383. - Simon Plouffe, Sep 15 2025

Crossrefs

Cf. A029838, A029839, A029840, A029841, A029842, A029843.

Sequence in context: A302972 A115146 A340312 * A000730 A160534 A022699

Adjacent sequences: A029841 A029842 A029843 * A029845 A029846 A029847

Keyword

sign

Author

N. J. A. Sloane

Status

approved