A215552 a(n) = binomial(8*n,n)*(6*n+1)/(7*n+1).

1, 7, 104, 1748, 31000, 566618, 10559208, 199448964, 3804949176, 73143988775, 1414591812920, 27492340515912, 536480138597624, 10504551860174120, 206284010045343000, 4061109502392133464, 80126310234711780600, 1583953257985260802200, 31365436013686385802048

Offset: 0

Author

Alois P. Heinz, Aug 15 2012

Keywords

• nonn
• changed

Comments

Number of standard Young tableaux of shape [7n,n].

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..235
• Wikipedia, Young tableau.

Crossrefs

Column k=7 of A214776.

Programs

Maple

a:= n-> binomial(8*n,n)*(6*n+1)/(7*n+1):
seq(a(n), n=0..20);

Mathematica

Table[Binomial[8n,n] (6n+1)/(7n+1),{n,0,20}] (* Harvey P. Dale, Mar 30 2014 *)

Formula

a(n) = C(8*n,n)*(6*n+1)/(7*n+1).

a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(6*n+1). - Ilya Gutkovskiy, Nov 01 2017

a(n) ~ 3 * 4^(12*n+1) / (7^(7*n+3/2) * sqrt(Pi*n)). - Amiram Eldar, Aug 29 2025