YT cont

[Emeric Deutsch (RP)[M}]

Re: A047884. 
Obviously (after doublechecking!), 

Triangle of numbers a(n,k) = no. of self-inverse permutations 
on n letters in which the length of the longest increasing 
subsequence is k. 

Another reference:
D. Stanton and D. White, Constructive Combinatorics, Springer, 2986.

On Wed, 12 May 1999, N. J. A. Sloane wrote:

> in resposne to JHC's message, I have added an example to A047884:
> 
> %I A047884
> %S A047884 1,1,1,1,2,1,1,5,3,1,1,9,11,4,1,1,19,31,19,5,1,1,34,92,69,29,6,1,1,
> %T A047884 69,253,265,127,41,7,1,1,125,709,929,583,209,55,8,1,1,251,1936,3356,
> %U A047884 2446,1106,319,71,9,1,1,461,5336,11626,10484,5323,1904,461,89,10,1
> %N A047884 Triangle of numbers a(n,k) = no. of Young tableaux with n cells and k rows (1<=k<=
> n).
> %D A047884 W. Fulton, Young Tableaux, Cambridge, 1997.
> %O A047884 1,5
> %K A047884 nonn,tabl,nice,easy
> %t A047884 Table[Plus@@( NumberOfTableaux/@ Reverse/@Union[Sort/@(Compositions[n-m,m]+1)]), {
> n,12},{m,n} ]
> %Y A047884 Row sums give A000085.
> %e A047884 1; 1,1; 1,2,1; 1,5,3,1; 1,9,11,4,1; ... For n=3 the 4 tableaux are
> %e A047884 1 2 3 . 1 2 . 1 3 . 1
> %e A047884 . . . . 3 . . 2 . . 2
> %e A047884 . . . . . . . . . . 3
> %A A047884 w.meeussen.vdmcc at vandemoortele.be
> 
> NJAS
>