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 A048603 Denominators of coefficients in function a(x) such that a(a(x)) = sin x. 11
 1, 12, 160, 40320, 71680, 1277337600, 79705866240, 167382319104000, 91055981592576000, 62282291409321984000, 4024394214140805120000, 5882770031248492462080000, 9076273762497674084352000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also denominators of coefficients in function a(x) such that a(a(x)) = sinh x. A recursion exists for coefficients, but is too complicated to process without a computer algebra system. REFERENCES W. C. Yang, Polynomials are essentially integer partitions, preprint, 1999 W. C. Yang, Composition equations, preprint, 1999 LINKS Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation \$A^{2^n}(x)=F(x)\$, arXiv:1302.1986 W. C. Yang, Derivatives are essentially integer partitions, Discrete Math., 222 (2000), 235-245. EXAMPLE x - x^3/12 - x^5/160 ... 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]] (* Jean-François Alcover, May 05 2011 *) CROSSREFS Cf. A048602, A048606. Sequence in context: A144346 A167558 A048609 * A275040 A109391 A296194 Adjacent sequences:  A048600 A048601 A048602 * A048604 A048605 A048606 KEYWORD frac,nonn,nice AUTHOR Winston C. Yang (yang(AT)math.wisc.edu) EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007 STATUS approved

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Last modified December 4 17:50 EST 2021. Contains 349526 sequences. (Running on oeis4.)