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%I #22 Sep 12 2023 08:30:36
%S 1,1,1,25,49,49,121,20449,20449,5909761,17631601,17631601,55190041,
%T 55190041,55190041,46414824481,154341336769,154341336769,427538329,
%U 585299972401,585299972401,983889253606081,3438962627443561,3438962627443561,7596668444022826249
%N Numerator of (binomial(2*n-2,n-1)/n!)^2.
%H G. C. Greubel, <a href="/A004936/b004936.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>
%F a(n) = numerator( (A000108(n-1)/(n-1)!)^2 ). - _G. C. Greubel_, Sep 12 2023
%t Numerator[Table[(Binomial[2n-2,n-1]/n!)^2,{n,30}]] (* _Harvey P. Dale_, May 30 2012 *)
%o (PARI) a(n) = numerator((binomial(2*n-2,n-1)/n!)^2); \\ _Michel Marcus_, Jul 14 2022
%o (Magma) [Numerator((Catalan(n-1)/Factorial(n-1))^2): n in [1..40]]; // _G. C. Greubel_, Sep 12 2023
%o (SageMath) [numerator((catalan_number(n-1)/factorial(n-1))^2) for n in range(1,41)] # _G. C. Greubel_, Sep 12 2023
%Y Cf. A000108, A005017 (denominators).
%K nonn,frac
%O 1,4
%A _N. J. A. Sloane_
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