A161581 a(n) = (3n)!/(n!(n+1)!(n+2)!).

21, 231, 3003, 43758, 692835, 11685817, 207157665, 3823000545, 72931087320, 1430571328200, 28734046963560, 589047962752980, 12292044987448215, 260543149635912165, 5599392250947235125, 121830987186399315825

Offset: 3

Author

Alexander Adamchuk, Jun 14 2009

Keywords

• nonn

Comments

3-d analog of the Catalan numbers A000108.

Links

• Winston de Greef, Table of n, a(n) for n = 3..704
• Eric Weisstein's World of Mathematics, Binomial Sums.
• Eric Weisstein's World of Mathematics, Central Binomial Coefficient.
• Eric Weisstein's World of Mathematics, Catalan Number.

Crossrefs

Cf. A000108, A005789, A006480.

Programs

Maple

A161581 := proc(n) (3*n)!/n!/(n+1)!/(n+2)! ; end: seq(A161581(n),n=3..40) ; # R. J. Mathar, Jun 16 2009
a := proc (n) options operator, arrow: factorial(3*n)/(factorial(n)*factorial(n+1)*factorial(n+2)) end proc: seq(a(n), n = 3 .. 20); # Emeric Deutsch, Jun 14 2009

Formula

a(n) = A006480(n)/((n+1)^2*(n+2)).

a(n) ~ 3^(3*n + 1/2) / (2*Pi*n^4). - Vaclav Kotesovec, Feb 21 2023

a(n) = (1/2)*A005789(n) for n >= 3. - Peter Bala, Mar 01 2023

D-finite with recurrence (n+2)*(n+1)*a(n) -3*(3*n-1)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Nov 22 2024

Extensions

Repetitions of information contained in other sequences removed by R. J. Mathar, Jun 16 2009

More terms from Emeric Deutsch, Jun 14 2009