A004824 Denominator of 2^n*(3*n-3)!/( ((n-1)!)^3 * (2*n)! ).

1, 1, 1, 3, 36, 900, 675, 66150, 6350400, 34292160, 857304000, 12966723000, 222286680000, 2366686281960000, 57983813908020000, 1581376742946000000, 2226578454067968000000, 55155529133626521600000, 114553791277532006400000, 3490915210814660428800000

Offset

1,4

Links

Table of n, a(n) for n=1..20.

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 Theorem.

Mathematica

a[n_] := Denominator[2^n * (3*n-3)! / (((n-1)!)^3*(2*n)!)]; Array[a, 20] (* Amiram Eldar, Oct 28 2025 *)

Crossrefs

Cf. A004677 (numerators).

Sequence in context: A227251 A326273 A224006 * A132912 A303866 A126447

Adjacent sequences: A004821 A004822 A004823 * A004825 A004826 A004827

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Typo in title corrected by Sean A. Irvine, Feb 08 2016

Status

approved