

A052135


Denominators of coefficients in function a(x) such that a(a(a(x))) = sin x.


3



1, 18, 1080, 408240, 29393280, 215550720, 648499737600, 953294614272000, 2333665215737856000, 7183021534041120768000, 232066849561328517120000, 723095875143672151080960000, 74189636789740762700906496000000
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OFFSET

0,2


COMMENTS

Also denominators of coefficients in function a(x) such that a(a(a(x))) = sinh x.


REFERENCES

W. C. Yang, Composition equations, preprint, 1999.


LINKS

Table of n, a(n) for n=0..12.


MATHEMATICA

n = 13; m = 2 n  1 (* m = maximal degree *); a[x_] = Sum[c[k] x^k, {k, 1, m, 2}] ; coes = DeleteCases[ CoefficientList[Series[a @ a @ a @ x  Sin[x], {x, 0, m}], x] // Rest , 0]; Do[s[k] = Solve[coes[[1]] == 0] // First; coes = coes /. s[k] // Rest, {k, 1, n}]
(CoefficientList[a[x] /. Flatten @ Array[s, n], x] // Denominator // Partition[#, 2] &)[[All, 2]]
(* JeanFrançois Alcover, May 04 2011 *)


CROSSREFS

Cf. A052132, A052134. See also A048602, A048603, etc.
Sequence in context: A301651 A159379 A323571 * A033518 A333006 A064564
Adjacent sequences: A052132 A052133 A052134 * A052136 A052137 A052138


KEYWORD

nonn,frac,easy,nice


AUTHOR

N. J. A. Sloane, Jan 22 2000


EXTENSIONS

More terms from Vladeta Jovovic, Jul 16 2002


STATUS

approved



