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%I #25 Sep 13 2023 08:50:38
%S 1,1,1,36,144,400,3600,2822400,16257024,32920473600,823011840000,
%T 8129341440000,292656291840000,3877578804363264,58642395498086400,
%U 844450495172444160000,54044831691036426240000,1161740555606493757440000,76817130615613056614400
%N Denominator of (binomial(2*n-2,n-1)/n!)^2.
%H G. C. Greubel, <a href="/A005017/b005017.txt">Table of n, a(n) for n = 1..270</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) = denominator( (A000108(n-1)/(n-1)!)^2 ). - _G. C. Greubel_, Sep 12 2023
%t Denominator[Table[(Binomial[2n-2,n-1]/n!)^2,{n,20}]] (* _Harvey P. Dale_, May 30 2012 *)
%o (PARI) a(n) = denominator((binomial(2*n-2,n-1)/n!)^2); \\ _Michel Marcus_, Jul 14 2022
%o (Magma) [Denominator((Catalan(n-1)/Factorial(n-1))^2): n in [1..40]]; // _G. C. Greubel_, Sep 12 2023
%o (SageMath) [denominator((catalan_number(n-1)/factorial(n-1))^2) for n in range(1,41)] # _G. C. Greubel_, Sep 12 2023
%Y Cf. A000108, A004936 (numerators).
%K nonn,frac
%O 1,4
%A _N. J. A. Sloane_
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