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EXAMPLE
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Given G(x) = x*(1+x)/(1-x):
G(x) = x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 2*x^6 +...
then the initial coefficients of the n-th iterations of G(x) begin:
n=1: [(1), 2, 2, 2, 2, 2, 2, 2, 2, ...];
n=2: [1,(4), 12, 32, 80, 196, 476, 1152, 2784, ...];
n=3: [1, 6,(30), 138, 602, 2542, 10518, 42994, ...];
n=4: [1, 8, 56,(368), 2320, 14216, 85368, 505312, ...];
n=5: [1, 10, 90, 770,(6370), 51450, 408202, 3194978, ...];
n=6: [1, 12, 132, 1392, 14272,(143372), 1418004, 13854368, ...];
n=7: [1, 14, 182, 2282, 27930, 335846,(3983518), 46736466, ...];
n=8: [1, 16, 240, 3488, 49632, 695312, 9623280,(131891776), ...]; ...;
the coefficients in parenthesis form the initial terms of this sequence.
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