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

1,4

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000139, A004824 (denominators).

Sequence in context: A371537 A138552 A258221 * A266656 A094955 A352292

Adjacent sequences: A004674 A004675 A004676 * A004678 A004679 A004680

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved