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A247386
Sum of the major index over all standard Young tableaux with n cells.
2
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
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
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Sep 15 2014
STATUS
approved