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A215542
a(n) = binomial(6*n,n)*(4*n+1)/(5*n+1).
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 15 2012
STATUS
approved