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Search: id:A007724
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| A007724 |
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Even minus odd extensions of truncated 3 X 2n grid diagram. |
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+0
2
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| 2, 12, 110, 1274, 17136, 255816, 4124406, 70549050, 1264752060, 23555382240, 452806924752, 8939481277552, 180551099694400, 3719061442253520, 77933728043586624, 1658001861319441280, 35749633305661574400
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Number of standard tableaux of shapes (n-1,n-1,k), k=0,1,...,n-1. Example: a(3)=12 because there are 2, 5 and 5 standard tableaux of shapes (2,2), (2,2,1) and (2,2,2), respectively. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 25 2004
Contribution from Joel Brewster Lewis (jblewis(AT)post.harvard.edu), Oct 05 2009: (Start)
Also the number of standard shifted Young tableaux of shape (n + 1, n, n - 1).
Also the number of 2143-avoiding up-down permutations of length 2n - 1. (End)
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LINKS
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F. Ruskey, Generating linear extensions of posets by transpositions, J. Combin. Theory, B 54 (1992), 77-101.
Dennis White, Sign-balanced posets
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FORMULA
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multinomial(3n; n-1, n, n+1)/(n(2n-1)(2n+1)).
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CROSSREFS
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Cf. A003121.
2143-avoiding up-down permutations of length 2n are given by A005789. [From Joel Brewster Lewis (jblewis(AT)post.harvard.edu), Oct 05 2009]
Sequence in context: A080446 A055897 A052563 this_sequence A126778 A158832 A102659
Adjacent sequences: A007721 A007722 A007723 this_sequence A007725 A007726 A007727
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KEYWORD
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nonn,easy
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AUTHOR
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fruskey(AT)cs.uvic.ca
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 24 1999
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