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EXAMPLE
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G.f.: A(x) = 1 - 2*x + 2*x^2 + 260*x^4 - 72384*x^5 +...
A(x) = 1 + log(eta(2*x)) + log(eta(4*x))^2/2! + log(eta(8*x))^3/3! +...
...
Given eta(x) = 1 - x - x^2 + x^5 + x^7 - x^12 - x^15 + x^22 +...
then a(n) is the coefficient of x^n in eta(x)^(2^n):
eta(x)^(2^0): [(1),-1,-1,0,0,1,0,1,0,0,0,0,-1,0,0,-1,0,0,0,0,..];
eta(x)^(2^1): [1,(-2),-1,2,1,2,-2,0,-2,-2,1,0,0,2,3,-2,2,...];
eta(x)^(2^2): [1,-4,(2),8,-5,-4,-10,8,9,0,14,-16,-10,-4,0,-8,...];
eta(x)^(2^3): [1,-8,20,(0),-70,64,56,0,-125,-160,308,0,110,0,...];
eta(x)^(2^4): [1,-16,104,-320,(260),1248,-3712,1664,6890,...];
eta(x)^(2^5): [1,-32,464,-3968,21576,(-72384),109120,215296,...];
eta(x)^(2^6): [1,-64,1952,-37632,512400,-5207936,(40618368),...]; ...
where terms in parenthesis form the initial terms of this sequence.
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