OFFSET
0,2
COMMENTS
Number of standard Young tableaux of shape [4n,n]. Also the number of binary words with 4n 1's and n 0's such that for every prefix the number of 1's is >= the number of 0's. The a(1) = 4 words are: 10111, 11011, 11101, 11110.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..285
Wikipedia, Young tableau
FORMULA
a(n) = C(5*n,n)*(3*n+1)/(4*n+1).
a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(3*n+1). - Ilya Gutkovskiy, Nov 01 2017
Recurrence: 8*n*(2*n - 1)*(3*n - 2)*(4*n - 1)*(4*n + 1)*a(n) = 5*(3*n + 1)*(5*n - 4)*(5*n - 3)*(5*n - 2)*(5*n - 1)*a(n-1). - Vaclav Kotesovec, Feb 03 2018
MAPLE
a:= n-> binomial(5*n, n)*(3*n+1)/(4*n+1):
seq(a(n), n=0..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 15 2012
STATUS
approved