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A094236
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Triangle read by rows: T(n,k) is the number of standard tableaux of shape (n,n,k) (0<=k<=n).
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0
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column k=0 is the sequence of Catalan numbers (A000108).
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FORMULA
| T(n, k)=(2n+k)!(n-k+2)(n-k+1)/[k!(n+2)!(n+1)! ] (0<=k<=n).
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EXAMPLE
| 1; 1,1; 2,5,5; 5,21,42,42; 14,84,252,462,462; 42,330,1320,3432,6006,6006;
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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);
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CROSSREFS
| Cf. A000108.
Sequence in context: A205396 A082086 A082084 * A205444 A073101 A130851
Adjacent sequences: A094233 A094234 A094235 * A094237 A094238 A094239
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004
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