

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
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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), 235245.


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
(* JeanFrançois 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



