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 A052134 Numerators of coefficients in function a(x) such that a(a(a(x))) = sinh x. 3
 1, 1, -7, 643, -13583, 29957, -24277937, 6382646731, 2027394133729, -10948179003324221, 177623182156029053, -126604967848904128751, -2640658729595838040517543, 423778395125199663867841, 134802774190189008299452419971 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES W. C. Yang, Composition equations, preprint, 1999. LINKS MATHEMATICA 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 *) CROSSREFS Cf. A052135. See also A048602, A048603, etc. Apart from signs, same as A052132? Sequence in context: A277839 A109542 A052132 * A101811 A092326 A074282 Adjacent sequences:  A052131 A052132 A052133 * A052135 A052136 A052137 KEYWORD sign,frac,easy,nice AUTHOR N. J. A. Sloane, Jan 22 2000 EXTENSIONS More terms from Vladeta Jovovic, Jul 16 2002 STATUS approved

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