A029840 Expansion of Product_{m>=1} ((1+q^(2*m-1))/(1+q^(2*m)))^3.

1, 3, 0, -5, 3, 9, -7, -15, 9, 27, -12, -45, 22, 66, -36, -99, 51, 153, -73, -222, 108, 311, -159, -441, 221, 624, -297, -863, 414, 1170, -575, -1584, 765, 2144, -1014, -2862, 1361, 3774, -1809, -4964, 2361, 6516, -3063, -8481

Offset

0,2

Links

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

Formula

G.f.: x^(3/8)*theta_2(sqrt(x))^3/theta_2(x)^3, where theta_() is the Jacobi theta function. - Ilya Gutkovskiy, Dec 04 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = 2 * exp(-3*Pi/8) * 2^(7/8) = A388379. - Simon Plouffe, Sep 15 2025

Crossrefs

Cf. A029838, A029839, A029841, A029842, A029843, A029844.

Sequence in context: A276408 A225744 A275393 * A144670 A370549 A011078

Adjacent sequences: A029837 A029838 A029839 * A029841 A029842 A029843

Keyword

sign

Author

N. J. A. Sloane

Status

approved