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Search: id:A056986
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| A056986 |
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Number of permutations on {1,...,n} containing any given pattern alpha in the symmetric group S_3. |
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+0
122
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| 0, 0, 1, 10, 78, 588, 4611, 38890, 358018, 3612004, 39858014, 478793588, 6226277900, 87175616760, 1307664673155, 20922754530330, 355687298451210, 6402373228089300, 121645098641568810, 2432902001612519580
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OFFSET
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1,4
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COMMENT
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This is well-defined because for all patterns alpha in S_3 the number of permutations in S_n avoiding alpha is the same (the Catalan numbers). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 05 2008
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REFERENCES
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R. Simion and F.W. Schmidt, Restricted Permutations, Europ. J. Comb., 6, 1985, 383-406.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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a(4)=10 because, taking, for example, the pattern alpha=321, we have 3214, 3241, 1432, 2431, 3421, 4213, 4132, 4231, 4312 and 4321.
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MATHEMATICA
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n!-Binomial[2n, n]/(n+1)
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CROSSREFS
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Sequence in context: A080618 A082136 A153596 this_sequence A006469 A081905 A016138
Adjacent sequences: A056983 A056984 A056985 this_sequence A056987 A056988 A056989
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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