OFFSET
0,5
COMMENTS
T(n,m)= number of standard tableaux of shape (n,m,m) (0<m<=n). - Emeric Deutsch, May 14 2004
FORMULA
C[0, 0, 0] := 1; C[x_, y_, z_] := 0 /; (x< y || y< z); C[u_, v_, 0] := (u+v)!/(u+1)!/(v)!(u-v+1); C[_, 0, 0] := 1; C[x_, y_, z_] := (C[x, y, z]= C[x-1, y, z]+C[x, y-1, z] +C[x, y, z-1]) /; (y<=x ||z<=y); Table[C[x, y, y], {x, 0, 10}, {y, 0, x}]
T(n, m)=(n+2m)!(n-m+1)(n-m+2)/[m!(m+1)!(n+2)! ] (0<=m<=n). - Emeric Deutsch, May 14 2004
EXAMPLE
1;
1,1;
1,3,5;
1,6,21,42;
1,10,56,210,462;
1,15,120,660,2574,6006;
...
T(2,1)=3 because in the first row of the diagram (2,1,1) we can have 12 or 13 or 14.
MAPLE
a:=proc(n, m) if m<=n then (n+2*m)!*(n-m+1)*(n-m+2)/m!/(m+1)!/(n+2)! else 0 fi end: seq(seq(a(n, m), m=0..n), n=0..9);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Nov 09 2001
STATUS
approved