A286133 Expansion of q^(-1/2) * eta(q^2) * eta(q^15) * eta(q^21) * eta(q^70) in powers of q.

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

Offset

0,35

Links

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

Michael Somos, A Remarkable eta-product Identity

Formula

G.f.: x^4 * Prod_{k>0} (1 - x^(2 * k)) * (1 - x^(15 * k)) * (1 - x^(21 * k)) * (1 - x^(70 * k)).

Maple

seq(coeff(series(x^4*mul((1-x^(2*k))*(1-x^(15*k))*(1-x^(21*k))*(1-x^(70*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^2]*eta[q^15]*eta[q^21]*eta[q^70], {q, 0, 50}], q] (* G. C. Greubel, Jul 28 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^2)*eta(q^15)*eta(q^21)*eta(q^70); concat([0, 0, 0, 0], Vec(A)) \\ G. C. Greubel, Jul 28 2018

Crossrefs

Cf. A286135.

Sequence in context: A287325 A336387 A358217 * A328248 A360158 A329885

Adjacent sequences: A286130 A286131 A286132 * A286134 A286135 A286136

Keyword

sign

Author

Seiichi Manyama, May 03 2017

Status

approved