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A048605
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Numerators of coefficients in function a(x) such that a(a(x)) = arctan x.
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1
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1, -1, 7, -43, 4489, -49897, 20130311, -319053131, 329796121169, -62717244921977, 14635852695795623, -33233512260583073, 149490010959849868177, -3562767949848393597053
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Recursion exists for coefficients, but is too complicated to use without a computer algebra system
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REFERENCES
| W. C. Yang, Polynomials are essentially integer partitions, preprint, 1999
W. C. Yang, Composition equations, preprint, 1999
W. C. Yang, Derivatives are essentially integer partitions, Discrete Math., 222 (2000), 235-245.
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EXAMPLE
| x - x^3/6 + x^5 * 7/120 + ...
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MATHEMATICA
| n = 28; a[x_] = Sum[c[k] k! x^k, {k, 1, n, 2}];
sa = Series[a[x], {x, 0, n}];
coes = CoefficientList[ComposeSeries[sa, sa] - Series[ArcTan[x], {x, 0, n}], x] // Rest;
eq = Reduce[((# == 0) & /@ coes)]; Table[c[k] k!, {k, 1, n, 2}] /. First[Solve[eq]] // Numerator
(* From Jean-François Alcover, Apr 26 2011 *)
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CROSSREFS
| Cf. A048604.
Sequence in context: A065786 A015463 A177507 * A165210 A162454 A203210
Adjacent sequences: A048602 A048603 A048604 * A048606 A048607 A048608
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KEYWORD
| frac,sign,nice
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AUTHOR
| Winston C. Yang (yang(AT)math.wisc.edu)
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