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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

Table of n, a(n) for n=0..13.

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-Fran├žois 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 April 23 18:45 EDT 2017. Contains 285329 sequences.