This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.