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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 60*x^3 + 2480*x^4 + 242296*x^5 +...
A(x) = 1 + x*[1 + log(A(2x)^2) + log(A(4x)^2)^2/2! + log(A(8x)^2)^3/3! + log(A(16x)^2)^4/4! + log(A(32x)^2)^5/5! +...].
Coefficients in the 2^n-th powers of A(x) begin:
A^(2^0)=[1, 1, 4, 60, 2480, 242296, 53763904, 28363717952,...];
A^(2^1)=[(1), 2, 9, 128, 5096, 490032, 108035840, 56837199680,...];
A^(2^2)=[1,(4), 22, 292, 10785, 1002752, 218139920, 114116667872,...];
A^(2^3)=[1, 8,(60), 760, 24390, 2104632, 444861660, 230028874632,...];
A^(2^4)=[1, 16, 184,(2480), 64540, 4690704, 926901832,...];
A^(2^5)=[1, 32, 624, 10848,(242296), 12359328, 2033807312,...];
A^(2^6)=[1, 64, 2272, 61632, 1568240,(53763904), 5278676128,...];
A^(2^7)=[1, 128, 8640, 414080, 16187360, 588318336,(28363717952),...];
A^(2^8)=[1, 256, 33664, 3040000, 213028800, 12475903232, 658516757120,(41396018951936),...]; ...
where the diagonal terms in parenthesis form this sequence (shift left).
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