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%I #7 Jul 18 2018 02:40:44
%S 1,1,1,-1,-1,1,0,1,-3,-1,0,-1,2,-4,-1,-1,-2,1,-4,1,0,0,4,1,1,2,5,4,2,
%T -1,0,1,0,6,0,-1,2,-4,2,-1,2,-4,-8,0,3,0,-4,-1,1,1,-2,-2,-6,1,0,-4,-4,
%U -6,8,1,-2,8,-8,-1,-2,0,0,-6,4,4,-8,1,2,2,1,4,0,2,8,1,1,-6,8,4,2,-4,2,0,2,-1,0,0,0,0,4,1,2,9,0,-1,10,6,8,2,0
%N Expansion of F(q)*F(q^5) where F(q) = eta(q^2)*eta(q^3)^3 / (eta(q)*eta(q^6)).
%H G. C. Greubel, <a href="/A122779/b122779.txt">Table of n, a(n) for n = 1..1500</a>
%F Euler transform of period 30 sequence [ 1, 0, -2, 0, 2, -2, 1, 0, -2, 0, 1, -2, 1, 0, -4, 0, 1, -2, 1, 0, -2, 0, 1, -2, 2, 0, -2, 0, 1, -4, ...].
%t eta[q_] := q^(1/24)*QPochhammer[q]; F[q_]:= eta[q^2]*eta[q^3]^3/(eta[q]*eta[q^6]); a:= CoefficientList[Series[F[q]*F[q^5], {q, 0, 100}], q]; Table[a[[n]], {n, 2, 50}] (* _G. C. Greubel_, Jul 18 2018 *)
%o (PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); A=eta(x^2+A)*eta(x^3+A)^3/eta(x+A)/eta(x^6+A); A=A*subst(A+x*O(x^(n\5)),x,x^5); polcoeff(A,n))}
%Y A122777(n)=a(2n).
%K sign
%O 1,9
%A _Michael Somos_, Sep 10 2006