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EXAMPLE
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E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 56*x^4/4! + 536*x^5/5! + ...
where A(x) = 1 + 8*x*A(x)/(Pi^2 - 4*x^2*A(x)^2) + 8*x*A(x)/(9*Pi^2 - 4*x^2*A(x)^2) + 8*x*A(x)/(25*Pi^2 - 4*x^2*A(x)^2) + 8*x*A(x)/(49*Pi^2 - 4*x^2*A(x)^2) + ...
The coefficients of x^n/n! in initial powers of G(x) = 1 + tan(x) begin:
G^1: [(1), 1, 0, 2, 0, 16, 0, 272, 0, 7936, ...];
G^2: [1,(2), 2, 4, 16, 32, 272, 544, 7936, ...];
G^3: [1, 3, (6), 12, 48, 168, 816, 4512, 23808, ...];
G^4: [1, 4, 12,(32), 120, 544, 2592, 15872, 96000, ...];
G^5: [1, 5, 20, 70, (280), 1400, 7520, 46720, 321280, ...];
G^6: [1, 6, 30, 132, 600, (3216), 19200, 125952, 925440, ...];
G^7: [1, 7, 42, 224, 1176, 6832, (44352), 312704, 2424576, ...];
G^8: [1, 8, 56, 352, 2128, 13568, 94976, (719872), 5907328, ...];
G^9: [1, 9, 72, 522, 3600, 25344, 191232, 1552752, (13518720), ...]; ...
where coefficients in parenthesis form initial terms of this sequence:
[1/1, 2/2, 6/3, 32/4, 280/5, 3216/6, 44352/7, 719872/8, 13518720/9, ...].
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