A215542 a(n) = binomial(6*n,n)*(4*n+1)/(5*n+1).

1, 5, 54, 663, 8602, 115101, 1570800, 21732542, 303719922, 4277470470, 60610884906, 863102246760, 12340998865104, 177064708142315, 2547927647834040, 36757054103054076, 531436857842656610, 7698470087956704210, 111712846834848074340, 1623556455926349703605

Offset: 0

Author

Alois P. Heinz, Aug 15 2012

Keywords

• nonn
• changed

Comments

Number of standard Young tableaux of shape [5n,n].

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..260
• Wikipedia, Young tableau.

Crossrefs

Column k=5 of A214776.

Programs

Maple

a:= n-> binomial(6*n,n)*(4*n+1)/(5*n+1):
seq(a(n), n=0..20);

Mathematica

Table[Binomial[6n,n] (4n+1)/(5n+1),{n,0,30}] (* Harvey P. Dale, Mar 06 2014 *)

Formula

a(n) = C(6*n,n)*(4*n+1)/(5*n+1).

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

Recurrence: 5*n*(4*n - 3)*(5*n - 3)*(5*n - 2)*(5*n - 1)*(5*n + 1)*a(n) = 72*(2*n - 1)*(3*n - 2)*(3*n - 1)*(4*n + 1)*(6*n - 5)*(6*n - 1)*a(n-1). - Vaclav Kotesovec, Feb 03 2018

a(n) ~ 3^(6*n+1/2) * 4^(3*n+1) / (5^(5*n+3/2) * sqrt(Pi*n)). - Amiram Eldar, Aug 29 2025