Young Tableaux counted

[vdmcc]

there do not seem to be much of them in EIS.
Are they sufficiently well known & used to merit more enumerative attention?
A000085 is their count , known as "Self-inverse permutations on n letters:
a(n) = a(n-1) + (n-1)a(n-2)."

this can be taken apart into a triangular table by counting them
as "number of Young Tableaux per partition of n in exactly m parts"

The triangular table is:
{
{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},
{1,69,253,265,127,41,7,1},
{1,125,709,929,583,209,55,8,1},
{1,251,1936,3356,2446,1106,319,71,9,1},
{1,461,5336,11626,10484,5323,1904,461,89,10,1},
{1,923,14587,41117,43363,26069,10275,3057,639,109,11,1}
}

Table[Plus@@(
      NumberOfTableaux/@ Reverse/@Union[Sort/@(Compositions[n-m,m]+1)]),{n,
    12},{m,n} ]

anyone vaguely interested?

w.meeussen.vdmcc at vandemoortele.be
tel  +32 (0) 51 33 21 11
fax +32 (0) 51 33 21 75