|
|
A123555
|
|
Number of standard Young tableaux of type (n+1,n,n-1).
|
|
4
|
|
|
0, 2, 16, 168, 2112, 30030, 466752, 7759752, 135980416, 2485891980, 47052314400, 916847954880, 18311313000960, 373542610526280, 7761573156274560, 163893933165976200, 3510476121410184960, 76151734612882397700, 1670824967127762045600, 37036620104665392010800, 828632324276985756528000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
For n > 0, a(n) is the number of up-down permutations of length 2n + 1 with no four-term increasing subsequence. Equivalently, this is the number of up-down permutations of length 2n + 1 with no four-term decreasing subsequence; the number of down-up permutations of length 2n + 1 with no four-term increasing subsequence; and the number of down-up permutations of length 2n + 1 with no four-term decreasing subsequence. (An up-down permutation is one whose descent set is {2, 4, 6, ...}.). - Joel B. Lewis, Oct 05 2009
|
|
REFERENCES
|
For definition see James and Kerber, Representation Theory of Symmetric Group, Addison-Wesley, 1981, p. 107.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 16*(3*n)!/((n-1)!*(n+1)!*(n+3)!).
(n-1)*(n+3)*(n+1)*a(n) -3*n*(3*n-1)*(3*n-2)*a(n-1)=0, n>1. - R. J. Mathar, Aug 10 2015
G.f.: 2x*3F2(5/3,4/3,2;3,5;27x). - R. J. Mathar, Aug 10 2015
|
|
MATHEMATICA
|
f[n_]:=16 (3 n)!/((n-1)! (n+1)! (n+3)!)
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Table[ NumberOfTableaux@ {n + 1, n, n - 1}, {n, 0, 17}] (* Robert G. Wilson v *)
|
|
PROG
|
(PARI) for(n=0, 25, print1(16*(3*n)!/((n-1)!*(n+1)!*(n+3)!), ", ")) \\ G. C. Greubel, Oct 15 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Amitai Regev (amitai.regev(AT)weizmann.ac.il), Nov 15 2006
|
|
STATUS
|
approved
|
|
|
|