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AlladiWeight on IntegerPartition ​

The last part times the product over consecutive parts of the gap less 1.

On IntegerPartition

Called as CombinatorialStat(x, "AlladiWeight"). The head's page has its examples.

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Distribution

Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.

FindStat St000477

The weight of a partition according to Alladi.

ObjectValue
[2]2
[3]3
[4]4
[5]5
[6]6
[7]7
[8]8
[9]9

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000477 has the rest.