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A052132
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Numerators of coefficients in function a(x) such that a(a(a(x))) = sin x.
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2
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1, -1, -7, -643, -13583, -29957, -24277937, -6382646731, 2027394133729, 10948179003324221, 177623182156029053, 126604967848904128751, -2640658729595838040517543, -423778395125199663867841
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| W. C. Yang, Composition equations, preprint, 1999.
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MATHEMATICA
| n = 14; 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] // Numerator // Partition[#, 2] &)[[All, 2]]
(* From Jean-François Alcover, May 4 2011 *)
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CROSSREFS
| Cf. A052135. See also A048602, A048603, etc.
Apart from signs, same as A052134?
Sequence in context: A047942 A175601 A109542 * A052134 A101811 A092326
Adjacent sequences: A052129 A052130 A052131 * A052133 A052134 A052135
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KEYWORD
| sign,frac,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 22 2000
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EXTENSIONS
| More terms from R. J. Mathar, coded equivalent to A052136 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 09 2009
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