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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, 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; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Column k=0 is the sequence of Catalan numbers (A000108).
LINKS
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: A205396 A082086 A082084 * A340777 A205444 A270705
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, May 30 2004
EXTENSIONS
Keyword tabl added by Michel Marcus, Apr 09 2013
STATUS
approved

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Last modified April 18 03:33 EDT 2024. Contains 371767 sequences. (Running on oeis4.)