A005017 Denominator of (binomial(2*n-2,n-1)/n!)^2.

1, 1, 1, 36, 144, 400, 3600, 2822400, 16257024, 32920473600, 823011840000, 8129341440000, 292656291840000, 3877578804363264, 58642395498086400, 844450495172444160000, 54044831691036426240000, 1161740555606493757440000, 76817130615613056614400

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 1..270
• 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, A004936 (numerators).

Programs

Magma

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

Mathematica

Denominator[Table[(Binomial[2n-2,n-1]/n!)^2,{n,20}]] (* Harvey P. Dale, May 30 2012 *)

PARI

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

SageMath

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

Formula

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