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A088691
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E.g.f.: A(x) = f(x*A(x)^2), where f(x) = exp(atan(x)).
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1, 1, 5, 47, 657, 12245, 285805, 8022555, 263276705, 9892965545, 418911700725, 19738761470375, 1024422336336625, 58067265415960125, 3569400983720767325, 236508279434832201875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Radius of convergence of A(x): r = exp(-Pi/2) = 0.207879576..., with A(r) = exp(Pi/4) = 2.19328..., where r = limit a(n)/a(n+1)*(n+1) as n->infinity. Radius of convergence is from a general formula based on an heuristic argument.
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FORMULA
| a(n) equals the coefficient of x^n in (exp(atan(x)))^(2n+1)/(2n+1).
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PROG
| (PARI) a(n)=n!*polcoeff((exp(atan(x)))^(2*n+1)+x*O(x^n), n, x)/(2*n+1)
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CROSSREFS
| Sequence in context: A006902 A180254 A127696 * A052802 A098799 A089155
Adjacent sequences: A088688 A088689 A088690 * A088692 A088693 A088694
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 06 2003
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