A014228 Product of 3 successive Catalan numbers.
2, 10, 140, 2940, 77616, 2378376, 80978040, 2982691140, 116776877360, 4800591267472, 205384736883872, 9084324900632800, 413286869105712000, 19262120149391220000, 916763612521908006000, 44440565510927197408500, 2189466044883038600910000
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..300
Programs
-
Maple
a:= proc(n) option remember; `if`(n=0, 2, 8*(2*n-1)*(2*n+1)*(2*n+3) *a(n-1) /((n+1)*(n+2)*(n+3))) end: seq(a(n), n=0..20); # Alois P. Heinz, Oct 20 2013 -
Mathematica
a[n_] := Times @@ CatalanNumber[{n, n+1, n+2}]; a /@ Range[0, 16] (* Jean-François Alcover, Dec 18 2020 *)
Formula
a(n) ~ 64^(n+1) / (Pi^(3/2) * n^(9/2)). - Vaclav Kotesovec, Aug 25 2014
From Amiram Eldar, Apr 02 2022: (Start)
a(n) = C(n)*C(n+1)*C(n+2), where C(n) = A000108(n) is the n-th Catalan number.
Sum_{n>=0} a(n)/4^(3*n+3) = 1/2 - 64*Gamma(7/4)^2/(45*Pi*Gamma(5/4)^2). (End)