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%I #27 Sep 08 2022 08:45:24
%S 0,0,0,3,14,40,90,175,308,504,780,1155,1650,2288,3094,4095,5320,6800,
%T 8568,10659,13110,15960,19250,23023,27324,32200,37700,43875,50778,
%U 58464,66990,76415,86800,98208,110704,124355,139230,155400,172938,191919
%N n*(n-1)*(n-2)*(n+3)/12.
%C Essentially the same as A050297 and A005701.
%C Also, the number of external intersections of the diagonals of a general n-gon = (A176145) - (A000332). - _Michel Lagneau_, Apr 21 2010
%H Vincenzo Librandi, <a href="/A117662/b117662.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: x^3*(3-x)/(1-x)^5. [_Colin Barker_, Jan 31 2012]
%p seq(n*(n-1)*(n-2)*(n+3)/12, n=0..40); # _Wesley Ivan Hurt_, Oct 10 2013
%t Table[n(n-1)(n-2)(n+3)/12, {n,0,100}] (* _Wesley Ivan Hurt_, Sep 26 2013 *)
%t CoefficientList[Series[x^3 (3 - x)/(1 - x)^5, {x, 0, 80}], x] (* _Vincenzo Librandi_, Oct 10 2013 *)
%o (Magma) [n*(n-1)*(n-2)*(n+3)/12: n in [0..50]]; // _Vincenzo Librandi_, Oct 10 2013
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, Apr 11 2006
%E Edited by _N. J. A. Sloane_, Apr 23 2006
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