A286134 Expansion of q^(-1/2) * eta(q^5) * eta(q^6) * eta(q^7) * eta(q^210) in powers of q.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 1, 2, -1, 2, 1, 0, 1, -1, 0, 0, 1, 0, 0, -1, 0, -2, -1, 0, 0, 1, -1, -2, 1, -1, -2, -2, 1, 0, 0, 0, 1, -2, 1, 0, 0, 2, 0, 0, 2, 1, -1, 1, 0, 0, 1, 1, -1, 0, 0, 3, 2, 2, 0, -1, 0, 1, -2

Offset

0,27

Links

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

Michael Somos, A Remarkable eta-product Identity

Formula

G.f.: x^9 * Product_{k>0} (1 - x^(5 * k)) * (1 - x^(6 * k)) * (1 - x^(7 * k)) * (1 - x^(210 * k)).

Maple

seq(coeff(series(x^9*mul((1-x^(5*k))*(1-x^(6*k))*(1-x^(7*k))*(1-x^(210*k)), k=1..n), x, n+1), x, n), n=0..150); # Muniru A Asiru, Jul 29 2018

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-1/2)* eta[q^5]*eta[q^6]*eta[q^7]*eta[q^210], {q, 0, 50}], q] (* G. C. Greubel, Jul 28 2018 *)

Prog

(PARI) q='q+O('q^50); A=eta(q^5)*eta(q^6)*eta(q^7)*eta(q^210); concat(vector(9), Vec(A)) \\ G. C. Greubel, Jul 28 2018

Crossrefs

Cf. A286135.

Sequence in context: A066057 A060588 A221167 * A336922 A276469 A272356

Adjacent sequences: A286131 A286132 A286133 * A286135 A286136 A286137

Keyword

sign

Author

Seiichi Manyama, May 03 2017

Status

approved