|
Search: id:A094236
|
|
|
| A094236 |
|
Triangle read by rows: T(n,k) is the number of standard tableaux of shape (n,n,k) (0<=k<=n). |
|
+0
1
|
|
| 1, 1, 1, 2, 5, 5, 5, 21, 42, 42, 14, 84, 252, 462, 462, 42, 330, 1320, 3432, 6006, 6006, 132, 1287, 6435, 21450, 51480, 87516, 87516, 429, 5005, 30030, 121550, 364650, 831402, 1385670, 1385670, 1430, 19448, 136136, 646646, 2309450, 6466460
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Column k=0 is the sequence of Catalan numbers (A000108).
|
|
FORMULA
|
T(n, k)=(2n+k)!(n-k+2)(n-k+1)/[k!(n+2)!(n+1)! ] (0<=k<=n).
|
|
EXAMPLE
|
1; 1,1; 2,5,5; 5,21,42,42; 14,84,252,462,462; 42,330,1320,3432,6006,6006;
|
|
MAPLE
|
T:=proc(n, k) if k>n then 0 else (2*n+k)!*(n-k+2)*(n-k+1)/k!/(n+2)!/(n+1)! fi end:seq(seq(T(n, k), k=0..n), n=0..9);
|
|
CROSSREFS
|
Cf. A000108.
Sequence in context: A078576 A082086 A082084 this_sequence A073101 A130851 A130856
Adjacent sequences: A094233 A094234 A094235 this_sequence A094237 A094238 A094239
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004
|
|
|
Search completed in 0.002 seconds
|
