A160832 Expansion of eta(q)*eta(q^2)*eta(q^4), where eta(q) = Product((1-q^m), m=1..oo).

1, -1, -2, 1, -1, 3, 3, -1, -1, -3, 2, -3, -2, 0, 0, 1, 2, 4, -3, 5, 3, -2, -4, 0, -2, -1, 1, -2, 2, -6, -3, -1, 3, 4, 5, -3, 2, 2, 3, 4, -7, 1, 4, -1, -3, 1, -4, 0, -4, 1, -2, 1, -2, -3, 1, -5, 0, 4, 1, 3, 5, 1, 4, -1, 7, -5, -2, 0, 0, -1, -2, 6, 8, -5, -5, -4, -3, 0, -1, 0, -6, -1, -3, 3, -3, 6, -2, -6, 6, 1, -4, 6, 0, 5, 6, 7, -5, -4, 4, -5, 2, 4, 6, -4, -3

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/4) * exp(7*Pi/24) * Pi^(3/4) * 2^(1/4) / Gamma(3/4)^3 = A388678. - Simon Plouffe, Sep 18 2025

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-7/24)* eta[q]*eta[q^2]*eta[q^4], {q, 0, 100}], q] (* G. C. Greubel, Apr 30 2018 *)

Prog

(PARI) q='q+O('q^50); Vec(eta(q)*eta(q^2)*eta(q^4)) \\ G. C. Greubel, Apr 30 2018

Crossrefs

Cf. A010815, A083650, A030189, A170925.

Sequence in context: A080396 A155582 A169946 * A351522 A157458 A174447

Adjacent sequences: A160829 A160830 A160831 * A160833 A160834 A160835

Keyword

sign

Author

N. J. A. Sloane and Gary W. Adamson, Feb 18 2010

Status

approved