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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 (list; graph; refs; listen; history; text; internal format)
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: A261389 A073389 A232061 * A036068 A162743 A224290

Adjacent sequences:  A247383 A247384 A247385 * A247387 A247388 A247389

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Sep 15 2014

STATUS

approved

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Last modified November 23 19:00 EST 2017. Contains 295128 sequences.