A215553 a(n) = binomial(9*n,n)*(7*n+1)/(8*n+1).

1, 8, 135, 2574, 51765, 1072764, 22664655, 485325150, 10495906641, 228723580800, 5014392953273, 110471247622008, 2443644577217025, 54238301397083592, 1207358254510786125, 26943600312354592800, 602594302548520646793, 13502992968597378745800

Offset: 0

Author

Alois P. Heinz, Aug 15 2012

Keywords

• nonn
• changed

Comments

Number of standard Young tableaux of shape [8n,n].

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..225
• Wikipedia, Young tableau.

Crossrefs

Column k=8 of A214776.

Programs

Maple

a:= n-> binomial(9*n,n)*(7*n+1)/(8*n+1):
seq(a(n), n=0..20);

Mathematica

a[n_] := Binomial[9*n,n]*(7*n+1)/(8*n+1); Array[a, 21, 0] (* Amiram Eldar, Aug 29 2025 *)

Formula

a(n) = C(9*n,n)*(7*n+1)/(8*n+1).

a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(7*n+1). - Ilya Gutkovskiy, Nov 01 2017

a(n) ~ 7 * 3^(18*n+1) / (2^(24*n+5) * sqrt(Pi*n)). - Amiram Eldar, Aug 29 2025