The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A014228 Product of 3 successive Catalan numbers. 4
 2, 10, 140, 2940, 77616, 2378376, 80978040, 2982691140, 116776877360, 4800591267472, 205384736883872, 9084324900632800, 413286869105712000, 19262120149391220000, 916763612521908006000, 44440565510927197408500, 2189466044883038600910000 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 23 20:31 EST 2024. Contains 370288 sequences. (Running on oeis4.)