%I #29 Sep 08 2022 08:44:33
%S 1,1,1,2,11,91,17,323,4807,3289,8671,11687,15283,10743949,15189721,
%T 21069613,1339779509,1339779509,101007559,101007559,4215217889,
%U 185371558793,8059632991,11489264051,815737747621,2203307656324321,41571842572157,3284175563200403
%N Numerator of 2^n*(3*n-3)!/( ((n-1)!)^3 * (2*n)! ).
%H G. C. Greubel, <a href="/A004677/b004677.txt">Table of n, a(n) for n = 1..1000</a>
%H Pavel Valtr, <a href="https://doi.org/10.1007/BF01271274">The probability that n random points in a triangle are in convex position</a>, Combinatorica 16 (1996), no. 4, 567-573.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Sylvester's Four-Point Problem.</a>
%t Table[Numerator[2^n*(3*n - 3)!/(((n - 1)!)^3*(2*n)!)], {n, 1, 50}] (* _G. C. Greubel_, Oct 12 2018 *)
%o (PARI) for(n=1,50, print1(numerator(2^n*(3*n - 3)!/(((n - 1)!)^3*(2*n)!)), ", ")) \\ _G. C. Greubel_, Oct 12 2018
%o (Magma) [Numerator(2^n*Factorial(3*n - 3)/((Factorial(n - 1))^3*Factorial(2*n))): n in [1..50]]; // _G. C. Greubel_, Oct 12 2018
%Y Cf. A000139, A004824 (denominators).
%K nonn,frac
%O 1,4
%A _N. J. A. Sloane_