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A120419
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A mysterious sequence.
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0
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1, 2, 22, 584, 28384, 2190128, 245762848, 37788392576, 7625538720256, 1954588198280192, 620259836756837632, 238698984906300222464
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A proper definition of this sequence is needed.
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.
I have the complete program code and can send it to anyone interested.
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REFERENCES
| H. Sussmann, Resultats recents sur les courbes optimales, Soc. Math. de France du 17 juin 2000
H. Sussmann and J. C. Willems, 300 Years of Optimal Control - IEEE Control Systems 1997 0272-1708l97l$10.0001997IEEE
H. Sussmann and J. C. Willems, The Brachistochrone Problem and Modern Control Theory - University of Groningen, May 1999
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LINKS
| Eric Weisstein's World of Mathematics, http://mathworld.wolfram.com/UmbralCalculus.html
Eric Weisstein's World of Mathematics, http://mathworld.wolfram.com/GeneratingFunction.html
Eric Weisstein's World of Mathematics, http://mathworld.wolfram.com/CauchyProduct.html
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FORMULA
| 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.
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CROSSREFS
| Sequence in context: A090730 A090313 A110129 * A177042 A132568 A015210
Adjacent sequences: A120416 A120417 A120418 * A120420 A120421 A120422
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KEYWORD
| uned,nonn,obsc,more
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AUTHOR
| Robert Wackensack (wackensack(AT)hotmail.com), Jul 09 2006
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