A051790 a(n) = C(n)*(C(n)-1)*(C(n)-2)/6, where C(n) are the Catalan numbers (A000108).

0, 0, 0, 10, 364, 11480, 374660, 13067054, 486345860, 19143687420, 789566607180, 33856987804640, 1500056631216220, 68334193148209300, 3188209413930298680, 151869731557849844790, 7367151946247774981940, 363173327612427801849380, 18161314108644668390867900, 919925047761524277211226180

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = binomial(binomial(2*n, n)/(n+1), 3). - Zerinvary Lajos, May 29 2006

a(n) ~ 2^(6*n-1) / (3 * n^(9/2) * Pi^(3/2)). - Amiram Eldar, Sep 23 2025

Maple

[seq (binomial(binomial(2*n, n)/(n+1), 3), n=0..24)]; # Zerinvary Lajos, May 29 2006

Mathematica

(#(#-1)(#-2))/6&/@CatalanNumber[Range[0, 20]] (* Harvey P. Dale, Oct 12 2014 *)

Crossrefs

Cf. A000108.

Sequence in context: A247335 A112694 A079914 * A220638 A119547 A117797

Adjacent sequences: A051787 A051788 A051789 * A051791 A051792 A051793

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 10 1999

Status

approved