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%I #9 May 10 2013 12:44:15
%S 1,1,-7,643,-13583,29957,-24277937,6382646731,2027394133729,
%T -10948179003324221,177623182156029053,-126604967848904128751,
%U -2640658729595838040517543,423778395125199663867841,134802774190189008299452419971
%N Numerators of coefficients in function a(x) such that a(a(a(x))) = sinh x.
%D W. C. Yang, Composition equations, preprint, 1999.
%t n = 15; m (* = maximal degree *)= 2n - 1; a[x_] = Sum[c[k]*x^k, {k, 1, m, 2}]; coes = DeleteCases[ CoefficientList[ Series[ a@a@a@x - Sinh[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] // Numerator // Partition[#, 2] &)[[All, 2]] (* _Jean-François Alcover_, Jan 04 2013 *)
%Y Cf. A052135. See also A048602, A048603, etc.
%Y Apart from signs, same as A052132?
%K sign,frac,easy,nice
%O 0,3
%A _N. J. A. Sloane_, Jan 22 2000
%E More terms from _Vladeta Jovovic_, Jul 16 2002
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