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

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

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)

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 *)

Crossrefs

Cf. A000108, A005568, A342288.

Sequence in context: A171214 A213955 A091990 * A059475 A156296 A003046

Adjacent sequences: A014225 A014226 A014227 * A014229 A014230 A014231

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved