A286133 - OEIS

%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