A004936 Numerator of (binomial(2*n-2,n-1)/n!)^2.

1, 1, 1, 25, 49, 49, 121, 20449, 20449, 5909761, 17631601, 17631601, 55190041, 55190041, 55190041, 46414824481, 154341336769, 154341336769, 427538329, 585299972401, 585299972401, 983889253606081, 3438962627443561, 3438962627443561, 7596668444022826249

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Pavel Valtr, The probability that $n$ random points in a triangle are in convex position, Combinatorica 16 (1996), no. 4, 567-573.
• Eric Weisstein's World of Mathematics, Sylvester's Four-Point Problem.

Crossrefs

Cf. A000108, A005017 (denominators).

Programs

Magma

[Numerator((Catalan(n-1)/Factorial(n-1))^2): n in [1..40]]; // G. C. Greubel, Sep 12 2023

Mathematica

Numerator[Table[(Binomial[2n-2,n-1]/n!)^2,{n,30}]] (* Harvey P. Dale, May 30 2012 *)

PARI

a(n) = numerator((binomial(2*n-2,n-1)/n!)^2); \\ Michel Marcus, Jul 14 2022

SageMath

[numerator((catalan_number(n-1)/factorial(n-1))^2) for n in range(1,41)] # G. C. Greubel, Sep 12 2023

Formula

a(n) = numerator( (A000108(n-1)/(n-1)!)^2 ). - G. C. Greubel, Sep 12 2023