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A048603
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Denominators of coefficients in function a(x) such that a(a(x)) = sin x.
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11
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1, 12, 160, 40320, 71680, 1277337600, 79705866240, 167382319104000, 91055981592576000, 62282291409321984000, 4024394214140805120000, 5882770031248492462080000, 9076273762497674084352000000
(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(x)) = sinh x.
Recursion exists for coefficients, but is too complicated to process without computer algebra system
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REFERENCES
| W. C. Yang, Polynomials are essentially integer partitions, preprint, 1999
W. C. Yang, Composition equations, preprint, 1999
W. C. Yang, Derivatives are essentially integer partitions, Discrete Math., 222 (2000), 235-245.
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EXAMPLE
| x - x^3/12 - x^5/160 ...
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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@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 5 2011 *)
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CROSSREFS
| Cf. A048602, A048606.
Sequence in context: A144346 A167558 A048609 * A109391 A138455 A024221
Adjacent sequences: A048600 A048601 A048602 * A048604 A048605 A048606
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KEYWORD
| frac,nonn,nice
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AUTHOR
| Winston C. Yang (yang(AT)math.wisc.edu)
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 15 2007
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