OFFSET
1,2
COMMENTS
a(n) is number of symmetric standard Young tableaux of shape (n,n,n). - Ran Pan, May 21 2015
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
Ran Pan, Problem 4, Project P.
FORMULA
f3 = floor((n+1)/2), f4 = floor(n/2);
a(n) = e(n) if n even otherwise o(n), where e(n) = 6*Gamma((3*n)/2))/((2 + n)*Gamma(1 + n/2)^2* Gamma(n/2)) and o(n) = ((1 + n)*Gamma(1/2 + (3*n)/2))/(2*Gamma((3 + n)/2)^3). - Peter Luschny, Sep 30 2018
EXAMPLE
Some solutions for n=5:
x 1 x x 0 x x 0 x x 4 x x 0 x x 1 x x 1 x
0 x 5 2 x 4 2 x 5 0 x 2 1 x 2 0 x 5 0 x 3
x 3 x x 1 x x 1 x x 5 x x 3 x x 2 x x 2 x
2 x 6 3 x 6 3 x 6 1 x 3 4 x 6 3 x 6 4 x 5
x 4 x x 5 x x 4 x x 6 x x 5 x x 4 x x 6 x
MAPLE
a := n -> `if`(irem(n, 2) = 0, ((1/2)*n+1)*factorial((3/2)*n)/ (factorial((1/2)*n+1)^2*factorial((1/2)*n)), factorial((3/2)*n+3/2)/ (factorial((1/2)*n+1/2)^3*((9/2)*n+3/2))): # Peter Luschny, Sep 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 07 2012
STATUS
approved