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%I #20 Mar 12 2021 22:24:48
%S 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,
%T 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,
%U 1,0,-2,0,0,0,0,0,0,0,0,0,0,-2,1,3,-1,-1,0,-1
%N Expansion of q^(-1/2) * eta(q^2) * eta(q^15) * eta(q^21) * eta(q^70) in powers of q.
%H Seiichi Manyama, <a href="/A286133/b286133.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^4 * Prod_{k>0} (1 - x^(2 * k)) * (1 - x^(15 * k)) * (1 - x^(21 * k)) * (1 - x^(70 * k)).
%p 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
%t 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 *)
%o (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
%Y Cf. A286135.
%K sign
%O 0,35
%A _Seiichi Manyama_, May 03 2017
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