This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A004936 #23 Feb 16 2025 08:32:28 %S A004936 1,1,1,25,49,49,121,20449,20449,5909761,17631601,17631601,55190041, %T A004936 55190041,55190041,46414824481,154341336769,154341336769,427538329, %U A004936 585299972401,585299972401,983889253606081,3438962627443561,3438962627443561,7596668444022826249 %N A004936 Numerator of (binomial(2*n-2,n-1)/n!)^2. %H A004936 G. C. Greubel, <a href="/A004936/b004936.txt">Table of n, a(n) for n = 1..1000</a> %H A004936 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 A004936 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Sylvester's Four-Point Problem.</a> %F A004936 a(n) = numerator( (A000108(n-1)/(n-1)!)^2 ). - _G. C. Greubel_, Sep 12 2023 %t A004936 Numerator[Table[(Binomial[2n-2,n-1]/n!)^2,{n,30}]] (* _Harvey P. Dale_, May 30 2012 *) %o A004936 (PARI) a(n) = numerator((binomial(2*n-2,n-1)/n!)^2); \\ _Michel Marcus_, Jul 14 2022 %o A004936 (Magma) [Numerator((Catalan(n-1)/Factorial(n-1))^2): n in [1..40]]; // _G. C. Greubel_, Sep 12 2023 %o A004936 (SageMath) [numerator((catalan_number(n-1)/factorial(n-1))^2) for n in range(1,41)] # _G. C. Greubel_, Sep 12 2023 %Y A004936 Cf. A000108, A005017 (denominators). %K A004936 nonn,frac %O A004936 1,4 %A A004936 _N. J. A. Sloane_