Young tableaux cont

[N. J. A. Sloane]

yes, i'm very interested, and i added this entry to the database

%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 corresponding to partiti
ons of n into exactly k parts.
%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; ...
%A A047884 (w.meeussen.vdmcc at vandemoortele.be)

and i modified A000085:

%I A000085 M1221 N0469
%S A000085 1,1,2,4,10,26,76,232,764,2620,9496,35696,140152,568504,2390480,
%T A000085 10349536,46206736,211799312,997313824,4809701440,23758664096,
%U A000085 119952692896,618884638912,3257843882624,17492190577600,95680443760576
%N A000085 Self-inverse permutations on n letters; Young tableaux with n cells.
%F A000085 a(n) = a(n-1) + (n-1)*a(n-2).
etc

NJAS