Search: id:A047884
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%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) = number of Young tableaux with n cells and 
               k rows (1<=k<=n); also number of self-inverse permutations on n letters 
               in which the length of the longest increasing subsequence is k.
%D A047884 W. Fulton, Young Tableaux, Cambridge, 1997.
%D A047884 D. Stanton and D. White, Constructive Combinatorics, Springer, 1986.
%H A047884 <a href="Sindx_Y.html#Young">Index entries for sequences related to Young 
               tableaux.</a>
%H A047884 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/papers/comb.ps">
               A combinatorial miscellany</a>
%e A047884 1; 1,1; 1,2,1; 1,5,3,1; 1,9,11,4,1; ...
%e A047884 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
%t A047884 Table[ Plus@@( NumberOfTableaux/@ Reverse/@Union[ Sort/@(Compositions[ 
               n-m, m ]+1) ]), {n, 12}, {m, n} ]
%Y A047884 Row sums give A000085. Cf. A049400, A049401.
%Y A047884 Sequence in context: A107735 A137570 A079213 this_sequence A124328 A055818 
               A106240
%Y A047884 Adjacent sequences: A047881 A047882 A047883 this_sequence A047885 A047886 
               A047887
%K A047884 nonn,tabl,nice,easy
%O A047884 1,5
%A A047884 wouter.meeussen(AT)pandora.be

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