A215551 a(n) = binomial(7*n,n)*(5*n+1)/(6*n+1).

1, 6, 77, 1120, 17199, 272272, 4395118, 71916768, 1188576675, 19794795118, 331670995656, 5584693695280, 94418718611490, 1601780734932840, 27253077978559384, 464859662065426880, 7946606112855555915, 136106890528701061242, 2335187812028912966125

Offset: 0

Author

Alois P. Heinz, Aug 15 2012

Keywords

• nonn
• changed

Comments

Number of standard Young tableaux of shape [6n,n].

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250
• Wikipedia, Young tableau.

Crossrefs

Column k=6 of A214776.

Programs

Maple

a:= n-> binomial(7*n,n)*(5*n+1)/(6*n+1):
seq(a(n), n=0..20);

Mathematica

Table[Binomial[7n,n] (5n+1)/(6n+1),{n,0,30}] (* Harvey P. Dale, Apr 30 2022 *)

Formula

a(n) = C(7*n,n)*(5*n+1)/(6*n+1).

a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(5*n+1). - Ilya Gutkovskiy, Nov 01 2017

a(n) ~ sqrt(3) * 5 * 7^(7*n+1/2) / (6^(6*n+2) * sqrt(Pi*n)). - Amiram Eldar, Aug 29 2025