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%I #26 Mar 12 2021 22:24:48
%S 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,
%T 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,
%U 2,0,0,2,1,-1,1,0,0,1,1,-1,0,0,3,2,2,0,-1,0,1,-2
%N Expansion of q^(-1/2) * eta(q^5) * eta(q^6) * eta(q^7) * eta(q^210) in powers of q.
%H Seiichi Manyama, <a href="/A286134/b286134.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^9 * Product_{k>0} (1 - x^(5 * k)) * (1 - x^(6 * k)) * (1 - x^(7 * k)) * (1 - x^(210 * k)).
%p 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
%t 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 *)
%o (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
%Y Cf. A286135.
%K sign
%O 0,27
%A _Seiichi Manyama_, May 03 2017
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