A004677 Numerator of 2^n*(3*n-3)!/( ((n-1)!)^3 * (2*n)! ).

1, 1, 1, 2, 11, 91, 17, 323, 4807, 3289, 8671, 11687, 15283, 10743949, 15189721, 21069613, 1339779509, 1339779509, 101007559, 101007559, 4215217889, 185371558793, 8059632991, 11489264051, 815737747621, 2203307656324321, 41571842572157, 3284175563200403

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. A000139, A004824 (denominators).

Programs

Magma

[Numerator(2^n*Factorial(3*n - 3)/((Factorial(n - 1))^3*Factorial(2*n))): n in [1..50]]; // G. C. Greubel, Oct 12 2018

Mathematica

Table[Numerator[2^n*(3*n - 3)!/(((n - 1)!)^3*(2*n)!)], {n, 1, 50}] (* G. C. Greubel, Oct 12 2018 *)

PARI

for(n=1,50, print1(numerator(2^n*(3*n - 3)!/(((n - 1)!)^3*(2*n)!)), ", ")) \\ G. C. Greubel, Oct 12 2018