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 A007724 Even minus odd extensions of truncated 3 X 2n grid diagram. 3
 2, 12, 110, 1274, 17136, 255816, 4124406, 70549050, 1264752060, 23555382240, 452806924752, 8939481277552, 180551099694400, 3719061442253520, 77933728043586630, 1658001861319441050, 35749633305661575300, 780123576993991461000, 17208112644166765652100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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, May 25 2004 From Joel B. Lewis, 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) LINKS J. B. Lewis, Pattern Avoidance for Alternating Permutations and Reading Words of Tableaux, Ph. D. Dissertation, Department of Mathematics, MIT, 2012. F. Ruskey, Generating linear extensions of posets by transpositions, J. Combin. Theory, B 54 (1992), 77-101. Dennis White, Sign-balanced posets FORMULA a(n) = multinomial(3n; n-1, n, n+1)/(n(2n-1)(2n+1)). a(n) ~ 3^(3*n+1/2) / (8*Pi*n^4). - Vaclav Kotesovec, Nov 13 2014 MATHEMATICA Table[(3*n)!/((n-1)!*n!*(n+1)!)/(n*(2*n-1)*(2*n+1)), {n, 2, 10}] (* Vaclav Kotesovec, Nov 13 2014 *) Table[(-1)^n HypergeometricPFQ[{-2 - 2 n, -2 n, -2 n - 1}, {2, 3}, 1], {n, 19}] (* Michael De Vlieger, Aug 22 2016 *) CROSSREFS Cf. A003121. 2143-avoiding up-down permutations of length 2n are given by A005789. - Joel B. Lewis, Oct 05 2009 After corrections, is very similar to A217800 and A241958. Sequence in context: A179493 A193268 A235601 * A217800 A241958 A217802 Adjacent sequences:  A007721 A007722 A007723 * A007725 A007726 A007727 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 24 1999 a(16)-a(18) corrected and a(19)-a(20) added by Alois P. Heinz, Aug 22 2016 STATUS approved

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)