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A225616 Number of tableaux of size n with major index (sum of descent set) equal to 1 mod n.

%I A225616 #33 Oct 18 2014 19:05:29
%S A225616 0,1,1,2,5,12,33,94,290,949,3245,11666,43731,170748,689957,2887816,
%T A225616 12458783,55406276,253142181,1187931688,5712032811,28131119950,
%U A225616 141645386201,728841245442,3827217750406,20499431084637,111876916513388,621831333931916,3516904353610571
%N A225616 Number of tableaux of size n with major index (sum of descent set) equal to 1 mod n.
%C A225616 Related to sum of characters of Lie(n).
%H A225616 Alois P. Heinz, <a href="/A225616/b225616.txt">Table of n, a(n) for n = 1..40</a>
%H A225616 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/transparencies/whouse.pdf">Whitehouse</a>
%F A225616 a(n) = Sum_{k=0..n(n-1)/2, k mod n=1} A232439(n,k). - _Alois P. Heinz_, Sep 15 2014
%t A225616 descentset[t_?TableauQ]:=Sort[Cases[t,i_Integer /; Position[t,i+1][[1,1]] > Position[t,i][[1,1]], {2}]];
%t A225616 majorindex[t_?TableauQ]:=Tr[descentset[t]];
%t A225616 Table[Tr[Count[Tableaux[#],(q_/;Mod[majorindex[q],Tr[#]]==1) ]& /@ Partitions[n]],{n,13}]
%Y A225616 Cf. A232439.
%K A225616 nonn
%O A225616 1,4
%A A225616 _Wouter Meeussen_, Aug 04 2013
%E A225616 Terms verified and more terms added, _Joerg Arndt_, Aug 04 2013
%E A225616 a(21)-a(24) from _Alois P. Heinz_, Aug 08 2013
%E A225616 a(25) from _Alois P. Heinz_, Aug 12 2013
%E A225616 a(26)-a(29) from _Alois P. Heinz_, Sep 15 2014