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%I #18 Oct 19 2021 14:56:15
%S 2,6,24,72,172,352,646,1094,1742,2642,3852,5436,7464,10012,13162,
%T 17002,21626,27134,33632,41232,50052,60216,71854,85102,100102,117002,
%U 135956,157124,180672,206772,235602,267346,302194,340342,381992,427352,476636
%N Third column of A071223.
%H Colin Barker, <a href="/A087645/b087645.txt">Table of n, a(n) for n = 2..1000</a>
%H Alvaro Carbonero, Beth Anne Castellano, Gary Gordon, Charles Kulick, Karie Schmitz, and Brittany Shelton, <a href="https://arxiv.org/abs/2106.14140">Permutations of point sets in R_d</a>, arXiv:2106.14140 [math.CO], 2021.
%H T. M. Cover, <a href="http://www.jstor.org/stable/2946294">The number of linearly inducible orderings of points in d-space</a>, SIAM J. Applied Math., 15 (1967), 434-439.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = A052149(n+1) + 2.
%F a(n) = (3*n^4-10*n^3+9*n^2-2*n+24)/12. - _Vladeta Jovovic_, Oct 26 2003
%F G.f.: -2*x^2*(x^4-4*x^3+7*x^2-2*x+1) / (x-1)^5. - _Colin Barker_, Dec 06 2014
%t CoefficientList[Series[-2 x^2*(x^4 - 4 x^3 + 7 x^2 - 2 x + 1)/(x - 1)^5, {x, 0, 38}], x][[3 ;; -1]] (* _Michael De Vlieger_, Oct 19 2021 *)
%o (PARI) Vec(-2*x^2*(x^4-4*x^3+7*x^2-2*x+1)/(x-1)^5 + O(x^100)) \\ _Colin Barker_, Dec 06 2014
%Y Cf. A052149, A071223.
%K nonn,easy
%O 2,1
%A _N. J. A. Sloane_, Oct 26 2003
%E More terms from _Vladeta Jovovic_, Oct 26 2003