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EXAMPLE
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Let F_n(x) denote the n-th iteration of F(x) = x/(1-x)^2;
then coefficients in the successive iterations of F(x) begin:
F_0: [(1), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
F(x):[1, (2), 3, 4, 5, 6, 7, 8, 9, 10, 11, ...];
F_2: [1, 4, (14), 46, 145, 444, 1331, 3926, 11434, 32960, ...];
F_3: [1, 6, 33, (174), 892, 4480, 22149, 108144, 522685, ...];
F_4: [1, 8, 60, 436, (3102), 21728, 150350, 1030158, 7000917, ...];
F_5: [1, 10, 95, 880, 8015, (72090), 642031, 5671962, ...];
F_6: [1, 12, 138, 1554, 17255, 189596, (2066073), 22361904, ...];
F_7: [1, 14, 189, 2506, 32830, 426244, 5494797, (70420126),...];
F_8: [1, 16, 248, 3784, 57132, 855840, 12740700, 188692708, (2782399406), ...]; ...
where the coefficients along the diagonal (shown in parenthesis)
form the initial terms of this sequence.
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