A247386 Sum of the major index over all standard Young tableaux with n cells.

0, 0, 1, 6, 30, 130, 570, 2436, 10696, 47160, 213660, 981640, 4625016, 22171656, 108766840, 543350640, 2772404160, 14402353216, 76294507536, 411229473120, 2257073089120, 12595032754080, 71481175794336, 412117251151936, 2413922299708800, 14352066564086400

Offset

0,4

Comments

Also sum of positions of all ascents in ballot sequences of length n, see example.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..40

Wikipedia, Young tableau

Formula

a(n) = Sum_{k=1..n*(n-1)/2} k*A232439(n,k).

Example

The 10 ballot sequences of length 4 are:
##   [ ballot seq] ascent positions  major index
01:  [ 1 1 1 1 ]   (none)            0
02:  [ 1 1 1 2 ]   3                 3
03:  [ 1 1 2 1 ]   2                 2
04:  [ 1 1 2 2 ]   2                 2
05:  [ 1 1 2 3 ]   2 + 3             5
06:  [ 1 2 1 1 ]   1                 1
07:  [ 1 2 1 2 ]   1 + 3             4
08:  [ 1 2 1 3 ]   1 + 3             4
09:  [ 1 2 3 1 ]   1 + 2             3
10:  [ 1 2 3 4 ]   1 + 2 + 3         6
The sum of the major indexes is a(4) = 30.

Crossrefs

Cf. A232439.

Sequence in context: A073389 A320744 A232061 * A317755 A036068 A162743

Adjacent sequences: A247383 A247384 A247385 * A247387 A247388 A247389

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Sep 15 2014

Status

approved