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%I M2968 #32 Sep 08 2022 08:44:33
%S 3,14,40,90,175,308,504,780,1155,1650,2288,3094,4095,5320,6800,8568,
%T 10659,13110,15960,19250,23023,27324,32200,37700,43875,50778,58464,
%U 66990,76415,86800,98208,110704,124355
%N Number of exterior points formed by extending diagonals of n-gon in general position.
%C See Gouyou-Beauchamps for an interpretation in terms of closed paths in the first quadrant of the square grid.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 74, Problem 8.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A005701/b005701.txt">Table of n, a(n) for n = 0..1000</a>
%H D. Gouyou-Beauchamps, <a href="http://dx.doi.org/10.1007/BFb0072513">Chemins sous-diagonaux et tableaux de Young</a>, pp. 112-125 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, Springer, 1986.
%H D. Gouyou-Beauchamps, <a href="/A005700/a005700.pdf">Chemins sous-diagonaux et tableaux de Young</a>, pp. 112-125 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, Springer, 1986. (Annotated scanned copy)
%H <a href="/index/Y#Young">Index entries for sequences related to Young tableaux.</a>
%F a(n) = (n+1)*(n+2)*(n+3)*(n+6)/12.
%F G.f.: (x-3)/(x-1)^5 [Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
%t CoefficientList[Series[(x - 3) / (x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 09 2013 *)
%o (Magma) [(n+1)*(n+2)*(n+3)*(n+6)/12: n in [0..50]]; // _Vincenzo Librandi_, Jun 09 2013
%o (PARI) a(n) = (n+1)*(n+2)*(n+3)*(n+6)/12; \\ _Michel Marcus_, Dec 16 2017
%Y A diagonal of the triangle in A179898.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, _Robert G. Wilson v_
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