A215554 a(n) = binomial(10*n,n)*(8*n+1)/(9*n+1).

1, 9, 170, 3625, 81510, 1888460, 44602348, 1067658735, 25810820750, 628737007195, 15408077648040, 379444514503119, 9382177773301060, 232775087755980000, 5792018711632340160, 144481310070897555910, 3611955405113118024990, 90470699668284950782170

Offset: 0

Author

Alois P. Heinz, Aug 15 2012

Keywords

• nonn
• changed

Comments

Number of standard Young tableaux of shape [9n,n].

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..215
• Wikipedia, Young tableau

Crossrefs

Column k=9 of A214776.

Programs

Maple

a:= n-> binomial(10*n,n)*(8*n+1)/(9*n+1):
seq(a(n), n=0..20);

Mathematica

Table[Binomial[10n,n] (8n+1)/(9n+1),{n,0,20}] (* Harvey P. Dale, Dec 19 2016 *)

Formula

a(n) = C(10*n,n)*(8*n+1)/(9*n+1).

a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(8*n+1). - Ilya Gutkovskiy, Nov 01 2017

a(n) ~ 2^(10*n+3) * 5^(10*n+1/2) / (3^(18*n+3) * sqrt(Pi*n)). - Amiram Eldar, Aug 29 2025