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

0, 1, 1, 2, 5, 12, 33, 94, 290, 949, 3245, 11666, 43731, 170748, 689957, 2887816, 12458783, 55406276, 253142181, 1187931688, 5712032811, 28131119950, 141645386201, 728841245442, 3827217750406, 20499431084637, 111876916513388, 621831333931916, 3516904353610571

Offset

1,4

Comments

Related to sum of characters of Lie(n).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..40

R. P. Stanley, Whitehouse

Formula

a(n) = Sum_{k=0..n(n-1)/2, k mod n=1} A232439(n,k). - Alois P. Heinz, Sep 15 2014

Mathematica

descentset[t_?TableauQ]:=Sort[Cases[t, i_Integer /; Position[t, i+1][[1, 1]] > Position[t, i][[1, 1]], {2}]];
majorindex[t_?TableauQ]:=Tr[descentset[t]];
Table[Tr[Count[Tableaux[#], (q_/; Mod[majorindex[q], Tr[#]]==1) ]& /@ Partitions[n]], {n, 13}]

Crossrefs

Cf. A232439.

Sequence in context: A191769 A221206 A281489 * A186739 A266292 A004114

Adjacent sequences: A225613 A225614 A225615 * A225617 A225618 A225619

Keyword

nonn

Author

Wouter Meeussen, Aug 04 2013

Extensions

Terms verified and more terms added, Joerg Arndt, Aug 04 2013

a(21)-a(24) from Alois P. Heinz, Aug 08 2013

a(25) from Alois P. Heinz, Aug 12 2013

a(26)-a(29) from Alois P. Heinz, Sep 15 2014

Status

approved