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%I #14 Mar 12 2021 22:24:44
%S 1,-1,-1,0,0,2,-1,0,0,0,1,0,0,0,0,0,-1,-2,0,0,0,0,2,0,0,0,1,0,0,0,0,0,
%T -1,0,0,0,0,2,0,0,-2,1,-1,0,0,-2,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,
%U 0,-2,1,0,0,0,-2,0,2,0,0,0,0,-2,0,0,1,1,0,0,0,-2,0,0,0,0,-2,0,0,0,0,0,0,2,0,0,0,2,0,0,0
%N Expansion of q^(-2/3)eta(q)eta(q^10)^2/eta(q^5) in powers of q.
%C Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
%H G. C. Greubel, <a href="/A117886/b117886.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of f(-q) * psi(q^5) in powers of q where f(),psi() are Ramanujan theta functions.
%F Euler transform of period 10 sequence [ -1, -1, -1, -1, 0, -1, -1, -1, -1, -2, ...].
%F G.f.: Product_{k>0} (1-x^k)*(1-x^(5k))*(1+x^(5k))^2.
%t eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-2/3)* eta[q]*eta[q^10]^2/eta[q^5], {q,0,50}], q] (* _G. C. Greubel_, Apr 17 2018 *)
%o (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^10+A)^2/eta(x^5+A), n))}
%o (PARI) q='q+O('q^99); Vec(eta(q)*eta(q^10)^2/eta(q^5)) \\ _Altug Alkan_, Apr 18 2018
%K sign
%O 0,6
%A _Michael Somos_, Oct 13 2006; corrected Jul 29 2007
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