A247386 - OEIS

%I #12 Feb 07 2017 10:27:11

%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