A024487 a(n) = (1/(4n+2))*M(3n; n,n,n).

1, 9, 120, 1925, 34398, 659736, 13302432, 278397405, 5996669250, 132166590270, 2967978162240, 67694635250424, 1564409223571600, 36561597688116000, 862822254602816640, 20535537339485077005, 492426552811873991850, 11886753074132473787250, 288645723487776840570000

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Number of standard Young tableaux of shape (n,n,{1}^n). - Alois P. Heinz, Apr 05 2013

Examples

			G.f. = x + 9*x^2 + 120*x^3 + 1925*x^4 + 34398*x^5 + 659736*x^6 + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A006480.

Programs

Maple

with(combinat):
a:= n-> multinomial(3*n, n$3)/(4*n+2):
seq(a(n), n=1..30);  # Alois P. Heinz, Apr 05 2013

Mathematica

a[ n_] := If[ n < 1, 0, (3 n)! / (n!^3 (4 n + 2))]; (* Michael Somos, Oct 25 2014 *)

PARI

{a(n) = if( n<1, 0, (3*n)! / (n!^3 * (4*n + 2)))}; /* Michael Somos, Oct 25 2014 */

Formula

a(n) ~ 3^(3*n+1/2) / (8*Pi*n^2). - Vaclav Kotesovec, Sep 06 2014

a(n) = A006480(n) / (4*n + 2) if n>0. - Michael Somos, Oct 25 2014

D-finite with recurrence: n^2*(2*n+1)*a(n) -3*(3*n-1)*(2*n-1)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Apr 27 2020

Extensions

Corrected and extended by Alois P. Heinz, Apr 05 2013