A217799
Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).
Original entry on oeis.org
1, 2, 16, 168, 2112, 30030, 466752, 7759752, 135980416
Offset: 0
A011553
Number of standard Young tableaux of type (n,n,n) whose (2,1) entry is odd.
Original entry on oeis.org
0, 2, 16, 182, 2400, 35310, 562848, 9540674, 169777504, 3142665968, 60099912320, 1181283863632, 23767586624960, 487947659276790, 10195163202404160, 216335108170636650, 4653803620322450880, 101343766487960918460, 2231268469684932939360, 49614581272087698764820
Offset: 1
giambruno(AT)ipamat.math.unipa.it
a(2) = 2 because the standard Young tableaux of type (2,2,2) whose (2,1) entry is odd are:
+---+ +---+
|1 2| |1 2|
|3 5| |3 4|
|4 6| |5 6|
+---+ +---+ - _Alois P. Heinz_, Feb 28 2012
- For definition see James and Kerber, Representation Theory of Symmetric Group, Addison-Wesley, 1981, p. 107.
Definition corrected by Amitai Regev (amitai.regev(AT)weizmann.ac.il), Nov 15 2006
A123691
a(n) = number of standard Young tableaux of type (n,n-1,n-1).
Original entry on oeis.org
1, 3, 21, 210, 2574, 36036, 554268, 9145422, 159352050, 2900207310, 54698315490, 1062710129520, 21172455657360, 431010704453400, 8939669081780520, 188478023140872630, 4031562420682009290, 87350519114776867950, 1914486941500560677250, 42397183540866961907100
Offset: 1
-
a:= n-> 6 *(3*n-2)! / (n! *(n-1)! *(n+2)!):
seq(a(n), n=1..25); # Alois P. Heinz, Apr 11 2012
-
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@{n, n - 1, n - 1}, {n, 18}]
Showing 1-3 of 3 results.
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