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

1,4

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, Vol. 16, No. 4 (1996), 567-573.

Eric Weisstein's World of Mathematics, Sylvester's Four-Point Problem.

Formula

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

Mathematica

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

Prog

(PARI) a(n) = denominator((binomial(2*n-2, n-1)/n!)^2); \\ Michel Marcus, Jul 14 2022
(Magma) [Denominator((Catalan(n-1)/Factorial(n-1))^2): n in [1..40]]; // G. C. Greubel, Sep 12 2023
(SageMath) [denominator((catalan_number(n-1)/factorial(n-1))^2) for n in range(1, 41)] # G. C. Greubel, Sep 12 2023

Crossrefs

Cf. A000108, A004936 (numerators).

Sequence in context: A380446 A368682 A016910 * A288488 A262789 A110754

Adjacent sequences: A005014 A005015 A005016 * A005018 A005019 A005020

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Status

approved