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Expansion of infinite product (q^12, q^12, q^6; q^5, q^7; q^12)_oo.
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%I #7 Apr 29 2023 08:09:45

%S 1,0,0,0,0,1,-1,1,0,0,1,-1,-1,-1,1,1,-1,0,0,0,0,0,0,-1,1,0,-1,-1,0,0,

%T 1,-1,-1,-1,0,2,0,0,0,0,0,-1,0,0,0,1,-2,0,-1,2,0,-1,1,-1,-1,0,1,0,0,1,

%U 0,-1,0,0,1,1,0,0,0,0,1,-1,-1,0,-1,1,0,0,1,-1,1,0,-1,0,1,1,0,1,-1,-1,1,0,1,0,1,0,-1,-1,1,0,1,0,1,0,-1

%N Expansion of infinite product (q^12, q^12, q^6; q^5, q^7; q^12)_oo.

%C |a(n)| < 3 if n < 1299, a(1299) = 3.

%F G.f.: Product_{k>0} (1-x^(12k))^2 * (1-x^(12k-6)) / ((1-x^(12k-5))*(1-x^(12k-7))).

%o (PARI) a(n)=local(A); if(n<0,0, A=1+x*O(x^n); polcoeff(prod(n=1,n\12+1,if(m=12*n,(A-x^m)^2*(A-x^(m-6))/(A-x^(m-5))/(A-x^(m-7)))),n))

%K sign

%O 0,36

%A _Michael Somos_, May 10 2004