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

3,1

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.

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

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

Crossrefs

Cf. A000108, A005789, A006480.

Sequence in context: A022586 A321952 A125409 * A350570 A069601 A173347

Adjacent sequences: A161578 A161579 A161580 * A161582 A161583 A161584

Keyword

nonn,changed

Author

Alexander Adamchuk, Jun 14 2009

Extensions

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

More terms from Emeric Deutsch, Jun 14 2009

Status

approved