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EXAMPLE
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Let F_n(x) denote the n-th iteration of F(x) = x + x^2 + x^3;
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, (1), 1, 0, 0, 0, 0, 0, 0, 0, 0, ...];
F_2: [1, 2, (4), 6, 8, 8, 6, 3, 1, 0, 0, ...];
F_3: [1, 3, 9, (24), 60, 138, 294, 579, 1053, 1767, 2739, ...];
F_4: [1, 4, 16, 60, (216), 744, 2460, 7818, 23910, 70446, 200160, ...];
F_5: [1, 5, 25, 120, 560, (2540), 11220, 48330, 203230, 835080, ...];
F_6: [1, 6, 36, 210, 1200, 6720, (36930), 199365, 1058175, ...];
F_7: [1, 7, 49, 336, 2268, 15078, 98826, (639093), 4080531, ...];
F_8: [1, 8, 64, 504, 3920, 30128, 228984, 1722084, (12821788),...];
F_9: [1, 9, 81, 720, 6336, 55224, 477000, 4085028, 34700940, (292495896), ...]; ...
where the coefficients along the diagonal (shown above in parenthesis)
form the initial terms of this sequence.
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