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 A052135 Denominators of coefficients in function a(x) such that a(a(a(x))) = sin x. 3

%I

%S 1,18,1080,408240,29393280,215550720,648499737600,953294614272000,

%T 2333665215737856000,7183021534041120768000,232066849561328517120000,

%U 723095875143672151080960000,74189636789740762700906496000000

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

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

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

%t 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}]

%t (CoefficientList[a[x] /. Flatten @ Array[s, n], x] // Denominator // Partition[#, 2] &)[[All, 2]]

%t (* _Jean-François Alcover_, May 04 2011 *)

%K nonn,frac,easy,nice

%O 0,2

%A _N. J. A. Sloane_, Jan 22 2000

%E More terms from _Vladeta Jovovic_, Jul 16 2002

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