SetPartitionsWithBlockSizesCount on IntegerPartition
The number of set partitions whose block sizes are the parts: the size factorial over the product of the factorials of the parts and of the multiplicities.
Called as CombinatorialStat(x, "SetPartitionsWithBlockSizesCount"). 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 St000049
The number of set partitions whose sorted block sizes correspond to the partition.
| Object | Value |
|---|---|
[] | 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/St000049 has the rest.