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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3*x^2/2! + 21*x^3/3! + 241*x^4/4! + 3951*x^5/5! +...
To illustrate how the terms are generated, form a table of coefficients of x^k/k!, k>=0, in (Integral A(x)^n dx)^n for n>=0 like so:
n=0: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
n=1: [0, 1, 1, 3, 21, 241, 3951, 85499, 2325205, 76860673, ...];
n=2: [0, 0, 2, 12, 88, 920, 13328, 254744, 6161568, 182632584, ...];
n=3: [0, 0, 0, 6, 108, 1710, 29700, 600642, 14344092, 403670790, ...];
n=4: [0, 0, 0, 0, 24, 960, 28800, 826560, 24665088, 793449216, ...];
n=5: [0, 0, 0, 0, 0, 120, 9000, 462000, 20958000, 922005000, ...];
n=6: [0, 0, 0, 0, 0, 0, 720, 90720, 7378560, 504040320, ...];
n=7: [0, 0, 0, 0, 0, 0, 0, 5040, 987840, 120022560, ...];
n=8: [0, 0, 0, 0, 0, 0, 0, 0, 40320, 11612160, ...];
n=9: [0, 0, 0, 0, 0, 0, 0, 0, 0, 362880, ...]; ...
then the column sums form the terms of this sequence.
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