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A117465 Denominator of -16/((n+2)*n*(n-2)*(n-4)).

%I A117465 #14 Jun 13 2015 00:52:05
%S A117465 9,0,15,0,105,24,945,120,3465,360,9009,840,19305,1680,36465,3024,
%T A117465 62985,5040,101745,7920,156009,11880,229425,17160,326025,24024,450225,
%U A117465 32760,606825,43680,801009,57120,1038345,73440,1324785,93024,1666665,116280
%N A117465 Denominator of -16/((n+2)*n*(n-2)*(n-4)).
%C A117465 I came up with the equation to help analyze the path to stable orbits of the logistic function
%C A117465 f(n+1) = k*n(1-n) for f(n) with n => 9, then f(n)*A072346(n-5) = A072346(n+3).
%C A117465 a(n) is the denominator of f(n). The numerator of f(n) is -1 if n is even, else -16.
%H A117465 Colin Barker, <a href="/A117465/b117465.txt">Table of n, a(n) for n = 1..1000</a>
%H A117465 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-10,0,10,0,-5,0,1).
%F A117465 a(n) = denominator of the reduced -16/(n*(n-2)*(n+2)*(n-4)).
%F A117465 a(2n) = A052762(n+1).
%F A117465 a(n) = 5*a(n-2) -10*a(n-4) +10*a(n-6) -5*a(n-8) +a(n-10) for n>15. - _R. J. Mathar_, Mar 27 2010
%F A117465 a(n) = -(-17+15*(-1)^n)*(n*(16-4*n-4*n^2+n^3))/32 for n>3. - _Colin Barker_, Nov 11 2014
%F A117465 G.f.: 3*x*(10*x^12-50*x^10+105*x^8-160*x^6-8*x^5-40*x^4+10*x^2-3) / ((x-1)^5*(x+1)^5). - _Colin Barker_, Nov 11 2014
%e A117465 f(5) = -16/(7*5*3*1) = -16/105, denominator a(5) = 105.
%e A117465 f(6) = -16/(8*6*4*2) = -1/24, denominator a(6) = 24.
%p A117465 f(n) := n -> (1/((n/4)+(n^2/4)-(n^3/16)-1))/n;
%t A117465 Join[{9,0,15,0},Denominator[Table[-(16/(n (n^3-4 n^2-4 n+16))), {n,5,40}]]]    (* _Harvey P. Dale_, Nov 06 2011 *)
%o A117465 (PARI) Vec(3*x*(10*x^12-50*x^10+105*x^8-160*x^6-8*x^5-40*x^4+10*x^2-3)/((x-1)^5*(x+1)^5) + O(x^100)) \\ _Colin Barker_, Nov 11 2014
%Y A117465 Cf. A052762, A072346.
%K A117465 frac,nonn,easy
%O A117465 1,1
%A A117465 _Steven J. Forsberg_, Apr 25 2006
%E A117465 Clearer definition from _R. J. Mathar_, Mar 27 2010