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Number of Young tableaux with n cells and k inversions.
0

%I #10 Mar 25 2014 16:09:22

%S 1,2,4,8,2,16,10,32,34,5,5,64,98,35,35,128,258,154,154,14,42,14

%N Number of Young tableaux with n cells and k inversions.

%C The sequence of rowsums is A000085, and the sequence of number of terms in each row is A002865.

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000017">The number of inversions of a tableau</a>

%e The irregular triangle begins

%e ..1

%e ..2

%e ..4

%e ..8...2

%e .16..10

%e .32..34...5...5

%e .64..98..35..35

%e 128.258.154.154..14..42..14

%e etc.

%Y Cf. A000041, A002865, A000079 (rowsum of A007318), A036799 (rowsum of A059797), A117506.

%K nonn,tabf,uned

%O 1,2

%A _Alford Arnold_, Nov 07 2009