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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

Table of n, a(n) for n=2..20.

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

Frank Ruskey

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 March 25 20:38 EDT 2019. Contains 321477 sequences. (Running on oeis4.)