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MultinomialOfParts on IntegerPartition ​

The multinomial coefficient of the size over the parts: the size factorial over the product of the factorials of the parts.

On IntegerPartition

Called as CombinatorialStat(x, "MultinomialOfParts"). 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 St000048

The multinomial of the parts of a partition.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000048 has the rest.