TwelveTimesMajorIndexVarianceOfStandardTableaux on IntegerPartition
Twelve times the variance of the major index over the standard tableaux: the sum of the first n squares, less the sum of the squared hook lengths.
Follows FindStat's description, whose Sage code does not parse; the values agree with it.
Called as CombinatorialStat(x, "TwelveTimesMajorIndexVarianceOfStandardTableaux"). The head's page has its examples.
Live
Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001178
Twelve times the variance of the major index among all standard Young tableaux of a partition.
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Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001178 has the rest.