%I A120419
%S A120419 1,2,22,584,28384,2190128,245762848,37788392576,7625538720256,
%T A120419 1954588198280192,620259836756837632,238698984906300222464
%N A120419 A mysterious sequence.
%C A120419 This is based on the derivatives of the real function g(x) := -1/f(x)^2. 
               They have been generated using the software Mathematica. I'm trying 
               to find a closed form.
%C A120419 I have the complete program code and can send it to anyone interested.
%D A120419 H. Sussmann, Resultats recents sur les courbes optimales, Soc. Math. 
               de France du 17 juin 2000
%D A120419 H. Sussmann and J. C. Willems, 300 Years of Optimal Control - IEEE Control 
               Systems 1997 0272-1708l97l$10.0001997IEEE
%D A120419 H. Sussmann and J. C. Willems, The Brachistochrone Problem and Modern 
               Control Theory - University of Groningen, May 1999
%H A120419 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               UmbralCalculus.html">http://mathworld.wolfram.com/UmbralCalculus.html</
               a>
%H A120419 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GeneratingFunction.html">http://mathworld.wolfram.com/GeneratingFunction.html</
               a>
%H A120419 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CauchyProduct.html">http://mathworld.wolfram.com/CauchyProduct.html</
               a>
%F A120419 The algorithm for the sequence is as follows: (step#) What to do (1) 
               Dj = 0, for each j, when j is odd (j=2k+1); (odd derivatives are 
               null) (3) D2 = -1*f(a)^-2; then b1 = 1; (the 2nd derivative) (4) 
               D4 = -2*f(a)^-5; (the 4th derivative) So b2 = 2; (5) D6 = -22*f(a)^-8; 
               (the 6th derivative) So b3 = 22; (6) D8 = -584*f(a)^-11 (the 8th 
               derivative) So b4 = 584; (8) D10= -28384*f(a)^-14 (the 10th derivative) 
               So b5 = 28384; and so on... (n) D2n= -bn*f(a)^-(3n-1) (the 2n-th 
               derivative) on general bn is unknown.
%Y A120419 Sequence in context: A090730 A090313 A110129 this_sequence A132568 A015210 
               A152558
%Y A120419 Adjacent sequences: A120416 A120417 A120418 this_sequence A120420 A120421 
               A120422
%K A120419 uned,nonn,obsc,more
%O A120419 0,2
%A A120419 Robert Wackensack (wackensack(AT)hotmail.com), Jul 09 2006