A030189 Expansion of eta(q)*eta(q^2)*eta(q^4)*eta(q^8).

1, -1, -2, 1, -1, 3, 3, -1, -2, -2, 4, -4, -1, -3, -3, 2, 2, 8, -3, 7, 6, -5, -7, 0, -3, -2, 2, -4, 1, -4, 1, -2, 3, 1, 7, -6, -3, 10, 10, 5, -7, -3, -4, 5, -8, 8, -1, -4, -1, -7, -9, 2, -3, -6, 2, -8, 14, 5, -6, 9, 12, 4, 6, 3, 8, -14, 2, -9, -3, -5, -10, 12, 6, 4, -2, -5, -3, 0

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Formula

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/32) * exp(5*Pi/8) * 2^(5/16) * Gamma(5/8)^4 * (3+2 * sqrt(2)) / (sqrt(2) * (2+sqrt(2))^(1/2))^(1/2) / Pi / Gamma(7/8)^4 = A388386. - Simon Plouffe, Sep 15 2025

Example

G.f. = q^(5/8) - q^(13/8) - 2*q^(21/8) + q^(29/8) - q^(37/8) + ...

Mathematica

QP:= QPochhammer; CoefficientList[Series[QP[q]*QP[q^2]*QP[q^4]*QP[q^8], {q, 0, 80}], q] (* G. C. Greubel, Dec 28 2019 *)

Prog

(PARI) my(x='x+O('x^80)); Vec(eta(x)*eta(x^2)*eta(x^4)*eta(x^8)) \\ G. C. Greubel, Dec 28 2019

Crossrefs

Sequence in context: A344912 A056670 A170925 * A275678 A273108 A306405

Adjacent sequences: A030186 A030187 A030188 * A030190 A030191 A030192

Keyword

sign

Author

N. J. A. Sloane

Status

approved