A024486 a(n) = (1/(2n+1))*Multinomial(3n; n,n,n).

1, 2, 18, 240, 3850, 68796, 1319472, 26604864, 556794810, 11993338500, 264333180540, 5935956324480, 135389270500848, 3128818447143200, 73123195376232000, 1725644509205633280, 41071074678970154010, 984853105623747983700, 23773506148264947574500

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

From Vaclav Kotesovec, Feb 19 2015: (Start)

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

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

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

(End)

a(n) = A006480(n)/(2n+1). - R. J. Mathar, Apr 27 2020

Mathematica

Table[Multinomial[n, n, n]/(2*n+1), {n, 0, 20}] (* Vaclav Kotesovec, Feb 19 2015 *)

Crossrefs

Sequence in context: A254999 A364167 A357603 * A052635 A366001 A259270

Adjacent sequences: A024483 A024484 A024485 * A024487 A024488 A024489

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Vaclav Kotesovec, Feb 19 2015

Status

approved