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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: 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

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Last modified February 21 17:15 EST 2020. Contains 332100 sequences. (Running on oeis4.)