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 A048604 Denominators of coefficients in function a(x) such that a(a(x)) = arctan(x). 1
 1, 6, 120, 1680, 362880, 7983360, 6227020800, 186810624000, 355687428096000, 121645100408832000, 51090942171709440000, 213653030899875840000, 1723467782592331776000000, 64431180179990249472000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A recursion exists for coefficients, but is too complicated to process without a computer algebra system. REFERENCES W. C. Yang, Polynomials are essentially integer partitions, preprint, 1999 W. C. Yang, Composition equations, preprint, 1999 LINKS Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation A^{2^n}(x) = F(x), arXiv:1302.1986 W. C. Yang, Derivatives are essentially integer partitions, Discrete Math., 222 (2000), 235-245. EXAMPLE x - x^3/6 + x^5 * 7/120 ... 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]] // Denominator (* Jean-François Alcover, Apr 26 2011 *) CROSSREFS Cf. A048605. Sequence in context: A066289 A170917 A115678 * A001516 A026337 A223629 Adjacent sequences:  A048601 A048602 A048603 * A048605 A048606 A048607 KEYWORD frac,nonn AUTHOR Winston C. Yang (yang(AT)math.wisc.edu) STATUS approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)