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EXAMPLE
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G.f.: A(x) = x + 2*x^2 - 12*x^3 + 56*x^4 - 12080*x^5 +...
Coefficients in the (2^n)-th iterations of A(x), n=0..7, begin:
[1, 2, -12, 56, -12080, -9802944, -31002027840, ...];
[1, 4, -16, 0, -23296, -19776000, -62160338944, ...];
[1, 8, 0, -256, -47104, -40198144, -124955000832, ...];
[1, 16, 128, 0, -106496, -83165184, -252519120896, ...];
[1, 32, 768, 14336, 0, -175898624, -516100718592, ...];
[1, 64, 3584, 184320, 8454144, 0, -1064313028608, ...];
[1, 128, 15360, 1777664, 199622656, 21145583616, 0, ...];
[1, 256, 63488, 15482880, 3730571264, 888894652416, 205351244791808, 0, ...];
where the zeros along the diagonal illustrate the property
that the coefficient of x^n in A_{2^(n-1)} is zero for n>2.
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