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A039797
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Triangle of numbers of Dyck paths.
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1
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1, 1, 1, 3, 3, 1, 14, 14, 6, 1, 84, 84, 40, 10, 1, 594, 594, 300, 90, 15, 1, 4719, 4719, 2475, 825, 175, 21, 1, 40898, 40898, 22022, 7865, 1925, 308, 28, 1, 379236, 379236, 208208, 78078, 21021, 4004, 504, 36, 1, 3711916, 3711916, 2068560, 804440, 231868, 49686
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| D. Gouyou-Beauchamps, Chemins sous-diagonaux et tableau de Young, pp. 112-125 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
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LINKS
| Index entries for sequences related to Young tableaux.
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FORMULA
| T(n, k)=(2n-k)!(2n-k+2)!(k+3)!/[(n-k)!(n-k+1)!k!(n+2)!(n+3)! ] for 0<=k<=n. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004
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MAPLE
| T:=(n, k)->(2*n-k)!*(2*n-k+2)!*(k+3)!/(n-k)!/(n-k+1)!/k!/(n+2)!/(n+3)!: seq(seq(T(n, k), k=0..n), n=0..10);
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MATHEMATICA
| Flatten[Table[((2n-k)!(2n-k+2)!(k+3)!)/((n-k)!(n-k+1)!k!(n+2)!(n+3)!), {n, 0, 10}, {k, 0, n}]] (* From Harvey P. Dale, Jan 27 2012 *)
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CROSSREFS
| Reflection of A039798.
Sequence in context: A094021 A062746 A115193 * A143171 A112292 A001497
Adjacent sequences: A039794 A039795 A039796 * A039798 A039799 A039800
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KEYWORD
| nonn,tabl,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004
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