A286132 - OEIS

%I #19 Mar 12 2021 22:24:48

%S 0,0,0,0,0,1,0,0,-1,0,0,-1,0,0,0,-1,0,0,1,-1,1,1,1,0,0,0,1,0,1,1,-1,1,

%T -1,-1,-1,-1,0,0,0,2,-2,-1,-1,1,1,-1,-2,0,-1,-1,0,1,0,1,0,2,-1,0,0,-1,

%U 2,0,0,0,2,-1,0,0,1,0,2,1,1,0,0,2,1,0,-1,-1,0

%N Expansion of q^(-1/2) * eta(q^3) * eta(q^10) * eta(q^14) * eta(q^105) in powers of q.

%H Seiichi Manyama, <a href="/A286132/b286132.txt">Table of n, a(n) for n = 0..10000</a>

%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/retaprod.html">A Remarkable eta-product Identity</a>

%F G.f.: x^5 * Prod_{k>0} (1 - x^(3 * k)) * (1 - x^(10 * k)) * (1 - x^(14 * k)) * (1 - x^(105 * k)).

%p seq(coeff(series(x^5*mul((1-x^(3*k))*(1-x^(10*k))*(1-x^(14*k))*(1-x^(105*k)),k=1..n), x,n+1),x,n),n=0..150); # _Muniru A Asiru_, Jul 29 2018

%t eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-1/2)* eta[q^3]*eta[q^10]*eta[q^14]*eta[q^105], {q, 0, 50}], q] (* _G. C. Greubel_, Jul 29 2018 *)

%o (PARI) q='q+O('q^50); A = eta(q^3)*eta(q^10)*eta(q^14)*eta(q^105); concat(vector(5), Vec(A)) \\ _G. C. Greubel_, Jul 29 2018

%Y Cf. A286135.

%K sign

%O 0,40

%A _Seiichi Manyama_, May 03 2017