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A247386 Sum of the major index over all standard Young tableaux with n cells. 2

%I

%S 0,0,1,6,30,130,570,2436,10696,47160,213660,981640,4625016,22171656,

%T 108766840,543350640,2772404160,14402353216,76294507536,411229473120,

%U 2257073089120,12595032754080,71481175794336,412117251151936,2413922299708800,14352066564086400

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

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

%H Alois P. Heinz, <a href="/A247386/b247386.txt">Table of n, a(n) for n = 0..40</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

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

%e The 10 ballot sequences of length 4 are:

%e ## [ ballot seq] ascent positions major index

%e 01: [ 1 1 1 1 ] (none) 0

%e 02: [ 1 1 1 2 ] 3 3

%e 03: [ 1 1 2 1 ] 2 2

%e 04: [ 1 1 2 2 ] 2 2

%e 05: [ 1 1 2 3 ] 2 + 3 5

%e 06: [ 1 2 1 1 ] 1 1

%e 07: [ 1 2 1 2 ] 1 + 3 4

%e 08: [ 1 2 1 3 ] 1 + 3 4

%e 09: [ 1 2 3 1 ] 1 + 2 3

%e 10: [ 1 2 3 4 ] 1 + 2 + 3 6

%e The sum of the major indexes is a(4) = 30.

%Y Cf. A232439.

%K nonn

%O 0,4

%A _Joerg Arndt_ and _Alois P. Heinz_, Sep 15 2014

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)