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PowerSumSymmetricFunctionAtOne on IntegerPartition ​

The power-sum symmetric function indexed by the partition, in as many variables as it has parts, all set to 1: the number of parts to its own power.

On IntegerPartition

Called as CombinatorialStat(x, "PowerSumSymmetricFunctionAtOne"). 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 St001563

The value of the power-sum symmetric function evaluated at 1.

ObjectValue
[1]1
[2]1
[3]1
[4]1
[5]1
[6]1
[7]1
[1,1]4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001563 has the rest.