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Number of permutations of [1..n] that can be drawn on a circle.
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%I #37 Feb 07 2024 03:38:54

%S 1,2,6,22,84,308,1090,3782,13000,44504,152102,519506,1773948,6056932,

%T 20680010,70606382,241065744,823050480,2810070734,9594182314,

%U 32756588164,111837988444,381838777906,1303679135238,4451038985688,15196797672872,51885112720758,177146855537986

%N Number of permutations of [1..n] that can be drawn on a circle.

%H Vincent Vatter and Steve Waton: <a href="https://doi.org/10.37236/710">On Points Drawn from a Circle</a>, Electronic J. Combin., 18 (2011), # P223.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,19,-10,2).

%F Vatter and Waton give a g.f.

%F G.f.: x*(2*x^5-4*x^4+5*x^3-9*x^2+5*x-1) / ((x-1)^3*(2*x^2-4*x+1)). - _Colin Barker_, Jul 05 2013

%t Rest[CoefficientList[Series[x (2x^5-4x^4+5x^3-9x^2+5x-1)/((x-1)^3 (2x^2- 4x+ 1)),{x,0,30}],x]] (* _Harvey P. Dale_, Sep 29 2013 *)

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Nov 29 2011