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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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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| 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
Mansour, Toufik; Yan, Sherry H. F.; and Yang, Laura L. M.; Counting occurrences of 231 in an involution. Discrete Math. 306 (2006), 564-572.
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LINKS
| 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
| 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.
G.f.: ((x^5-3*x^4+5*x^3-10*x^2+6*x-1)*(1-4*x)^(1/2) - 5*x^5+7*x^4-17*x^3+20*x^2-8*x+1)/(2*x^6) - Mark van Hoeij, Oct 25 2011.
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CROSSREFS
| Cf. A003517, A084249, A138159.
Sequence in context: A009134 A009137 A183900 * A069515 A056350 A056344
Adjacent sequences: A001086 A001087 A001088 * A001090 A001091 A001092
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KEYWORD
| nonn
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AUTHOR
| John Thomas Noonan [ noonan(AT)euclid.math.temple.edu ]
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