A014231 - OEIS

%I #9 Nov 17 2018 07:37:53

%S 1,5,70,1470,38808,1189188,40489020,1491345570,58388438680,

%T 2400295633736,102692368441936,4542162450316400,206643434552856000,

%U 9631060074695610000,458381806260954003000,22220282755463598704250,1094733022441519300455000,54717445279576990999935000

%N (Product of 3 successive Catalan numbers)/2.

%H Harvey P. Dale, <a href="/A014231/b014231.txt">Table of n, a(n) for n = 0..560</a>

%F a(n) = A014228(n)/2.

%p a:= proc(n) option remember; `if`(n=0, 1,

%p       8*(2*n-1)*(2*n+1)*(2*n+3)*a(n-1)/((n+1)*(n+2)*(n+3)))

%p     end:

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Oct 20 2013

%t Times@@@Partition[CatalanNumber[Range[0,20]],3,1]/2 (* _Harvey P. Dale_, Apr 10 2013 *)

%Y Cf. A000108.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.