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A052135
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Denominators of coefficients in function a(x) such that a(a(a(x))) = sin x.
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3
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1, 18, 1080, 408240, 29393280, 215550720, 648499737600, 953294614272000, 2333665215737856000, 7183021534041120768000, 232066849561328517120000, 723095875143672151080960000, 74189636789740762700906496000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also denominators of coefficients in function a(x) such that a(a(a(x))) = sinh x.
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REFERENCES
| W. C. Yang, Composition equations, preprint, 1999.
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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]]
(* From Jean-François Alcover, May 4 2011 *)
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CROSSREFS
| Cf. A052132, A052134. See also A048602, A048603, etc.
Sequence in context: A095786 A146197 A159379 * A033518 A064564 A152933
Adjacent sequences: A052132 A052133 A052134 * A052136 A052137 A052138
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KEYWORD
| nonn,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 Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 16 2002
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