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Search: id:A001089
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| A001089 |
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Number of permutations of [n] containing exactly 2 increasing subsequences of length 3. |
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+0
4
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| 0, 0, 0, 3, 24, 133, 635, 2807, 11864, 48756, 196707, 783750, 3095708, 12152855, 47500635, 185082495, 719559600, 2793121080, 10830450780, 41965864794, 162539516448, 629399492330, 2437072038302, 9437097796918
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OFFSET
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1,4
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REFERENCES
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M. Fulmek, Enumeration of permutations containing a prescribed number of occurrences of a pattern of length three, Adv. Appl. Math., 30, 2003, 607-632. also Arxiv CO/0112092
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LINKS
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J. Noonan and D. Zeilberger, [math/9808080] The Enumeration of Permutations With a Prescribed Number of ``Forbidden'' Patterns
T. Mansour and A. Vainshtein, Counting occurrences of 123 in a permutation.
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FORMULA
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Noonan and Zeilberger conjectured that a(n) = (59*n^2+117*n+100)/2/n/(2*n-1)/(n+5)*binomial(2*n,n-4). This was proved by Fulmek.
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CROSSREFS
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Cf. A003517, A084249, A138159.
Sequence in context: A151883 A009134 A009137 this_sequence A069515 A056350 A056344
Adjacent sequences: A001086 A001087 A001088 this_sequence A001090 A001091 A001092
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KEYWORD
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nonn
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AUTHOR
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John Thomas Noonan [ noonan(AT)euclid.math.temple.edu ]
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