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

0,2

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

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

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 *)

Crossrefs

Column k=5 of A214776.

Sequence in context: A087125 A110430 A110432 * A304322 A132619 A251583

Adjacent sequences: A215539 A215540 A215541 * A215543 A215544 A215545

Keyword

nonn

Author

Alois P. Heinz, Aug 15 2012

Status

approved