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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
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: A351862 A170917 A115678 * A001516 A350712 A378780
KEYWORD
frac,nonn
AUTHOR
Winston C. Yang (yang(AT)math.wisc.edu)
STATUS
approved