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A238094
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Triangle read by rows: T(n,k) (n >= 1, k >= 0) = number of Dyck paths of semilength k avoiding the pattern U^n D^n.
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0
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0, 1, 1, 1, 1, 1, 2, 4, 4, 1, 1, 2, 5, 13, 25, 25, 1, 1, 2, 5, 14, 41, 106, 196, 196, 1, 1, 2, 5, 14, 42, 131, 392, 980, 1764, 1764, 1, 1, 2, 5, 14, 42, 132, 428, 1380, 4068, 9864, 17424, 17424, 1, 1, 2, 5, 14, 42, 132, 429, 1429, 4797, 15489, 44649, 105633, 184041, 184041, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4861, 16714, 56749, 181258, 511225
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OFFSET
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1,7
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COMMENTS
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Row n has length 2n-1.
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LINKS
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Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, Julian West, The Dyck pattern poset, Discrete Math. 321 (2014), 12--23. MR3154009.
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EXAMPLE
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Triangle begins:
0,
1, 1, 1,
1, 1, 2, 4, 4,
1, 1, 2, 5, 13, 25, 25,
1, 1, 2, 5, 14, 41, 106, 196, 196,
1, 1, 2, 5, 14, 42, 131, 392, 980, 1764, 1764,
1, 1, 2, 5, 14, 42, 132, 428, 1380, 4068, 9864, 17424, 17424,
1, 1, 2, 5, 14, 42, 132, 429, 1429, 4797, 15489, 44649, 105633, 184041, 184041,
...
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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