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 A309205 Denominators of coefficients of odd powers of x in expansion of f(x) = x cos (x cos (x cos( ... . 3
 1, 2, 24, 720, 8064, 3628800, 479001600, 87178291200, 2988969984000, 6402373705728000, 2432902008176640000, 1124000727777607680000, 47726800133326110720000, 21225866375084507136000000, 60977668922342772100300800000, 265252859812191058636308480000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS f(x) satisfies f(x) = x * cos(f(x)), and the coefficients can be determined from this. Alternatively, a(n) can be written in terms of (2*n)! as a(n) = (2*n)!/A309206(n). LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 W. M. Gosper, Material from Bill Gosper's Computers & Math talk, M.I.T., 1989, i+38+1 pages, annotated and scanned, included with the author's permission. (There are many blank pages because about half of the original pages were two-sided, half were one-sided.) W. M. Gosper, Superposition of plots -4 f - x*cos(f): Newt:= unapply( f - G(f)/D(G)(f), f): ff:= x: for k from 1 to 5 do ff:= convert(series(Newt(ff), x, 2^(k+1)), polynom) od: seq(denom(coeff(ff, x, 2*i+1), i=0..31); # Robert Israel, Aug 18 2019 MATHEMATICA seq[n_] := Module[{p, k}, p = 1+O[x]; For[k = 2, k <= n, k++, p = Cos[x*p]]; p] // CoefficientList[#, x^2]& // Denominator; seq (* Jean-François Alcover, Sep 07 2019, from PARI *) PROG (PARI) \\ here F(n) gives n terms of power series. F(n)={my(p=1+O(x)); for(k=2, n, p=cos(x*p)); p} seq(n)={my(v=Vec(F(n))); vector(n, k, denominator(v[2*k-1]))} \\ Andrew Howroyd, Aug 17 2019 CROSSREFS Cf. A309204, A309206. Sequence in context: A069150 A323491 A046977 * A279331 A119699 A137891 Adjacent sequences:  A309202 A309203 A309204 * A309206 A309207 A309208 KEYWORD nonn,frac AUTHOR N. J. A. Sloane, Jul 28 2019 STATUS approved

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Last modified May 17 19:21 EDT 2022. Contains 353778 sequences. (Running on oeis4.)