A215688 Number of solid standard Young tableaux of shape [[3*n,3],[3]].

0, 192, 7020, 52808, 229680, 738192, 1950512, 4488180, 9314448, 17841200, 32050452, 54630432, 89126240, 140105088, 213336120, 315984812, 456821952, 646447200, 897527228, 1225048440, 1646584272, 2182577072, 2856634560, 3695840868, 4731082160, 5997386832

Offset: 0

Author

Alois P. Heinz, Aug 20 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
• Wikipedia, Young tableau

Crossrefs

Row n=3 of A176129.

Programs

Maple

a:= n-> `if`(n=0, 0, 32+(-312+(-362+(171+(657+(405+81*n)*n)*n)*n)*n)*n/4):
seq(a(n), n=0..40);

Formula

G.f.: 4*(8*x^6-41*x^5+105*x^4+181*x^3+1925*x^2+1419*x+48)*x/(1-x)^7.

a(n) = (3*n-1)*(3*n-2)*(3*n^2+13*n+16)*(3*n^2+5*n+4)/4 for n>0, a(0) = 0.