login
a(n) = (1/(2n+1))*Multinomial(3n; n,n,n).
1

%I #12 Apr 27 2020 12:16:17

%S 1,2,18,240,3850,68796,1319472,26604864,556794810,11993338500,

%T 264333180540,5935956324480,135389270500848,3128818447143200,

%U 73123195376232000,1725644509205633280,41071074678970154010,984853105623747983700,23773506148264947574500

%N a(n) = (1/(2n+1))*Multinomial(3n; n,n,n).

%F From _Vaclav Kotesovec_, Feb 19 2015: (Start)

%F a(n) = (3*n)! / ((2*n+1) * (n!)^3).

%F D-finite with recurrence: n^2*(2*n+1)*a(n) = 3*(2*n-1)*(3*n-2)*(3*n-1)*a(n-1).

%F a(n) ~ 3^(3*n+1/2) / (4*Pi*n^2).

%F (End)

%F a(n) = A006480(n)/(2n+1). - _R. J. Mathar_, Apr 27 2020

%t Table[Multinomial[n,n,n]/(2*n+1),{n,0,20}] (* _Vaclav Kotesovec_, Feb 19 2015 *)

%K nonn

%O 0,2

%A _Clark Kimberling_

%E More terms from _Vaclav Kotesovec_, Feb 19 2015