A052135 Denominators of coefficients in function a(x) such that a(a(a(x))) = sin x.

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

Offset: 0

Author

N. J. A. Sloane, Jan 22 2000

Keywords

• nonn
• frac
• easy
• nice

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.

Crossrefs

Cf. A052132, A052134. See also A048602, A048603, etc.

Programs

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]]
(* Jean-François Alcover, May 04 2011 *)

Extensions

More terms from Vladeta Jovovic, Jul 16 2002