A286131 Expansion of q^(-1/2) * eta(q) * eta(q^30) * eta(q^35) * eta(q^42) in powers of q.

0, 0, 0, 0, 1, -1, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 1, 0, 0, -3, 1, 0, 0, 0, -2, 0, -1, 1, 1, 1, 0, 0, 0, -1, 1, 1, -1, 0, 1, 0, -1, 1, 0, 0, -1, 0, 1, 0, -1, 1, -1, -2, -1, 0, 1, 1, 4, -1, -1, 1, 0, 0

Offset

0,40

Comments

Euler transform of a period 210 sequence. - Michael Somos, Nov 14 2019

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^k) * (1 - x^(30 * k)) * (1 - x^(35 * k)) * (1 - x^(42 * k)).

Example

G.f. = x^4 - x^5 - x^6 + x^9 + x^11 - x^16 - x^19 + x^26 + x^30 - x^34 + ... - Michael Somos, Nov 14 2019

Maple

seq(coeff(series(x^4*mul((1-x^k)*(1-x^(30*k))*(1-x^(35*k))*(1-x^(42*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]*eta[q^30]*eta[q^35]*eta[q^42], {q, 0, 50}], q] (* G. C. Greubel, Jul 29 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q)*eta(q^30)*eta(q^35)*eta(q^42); concat(vector(4), Vec(A)) \\ G. C. Greubel, Jul 29 2018
(PARI) {a(n) = n-=4; if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^30 + A) * eta(x^35 + A) * eta(x^42 + A), n))}; /* Michael Somos, Nov 14 2019 */

Crossrefs

Cf. A286135.

Sequence in context: A193525 A049828 A342557 * A285631 A316836 A058612

Adjacent sequences: A286128 A286129 A286130 * A286132 A286133 A286134

Keyword

sign

Author

Seiichi Manyama, May 03 2017

Status

approved