The number of partitions of with or fewer addends, or equivalently, into partitions with no element greater than . This function is denoted or . (Note that if " or fewer" is changed to "exactly " and "no element greater than " to "greatest element equal to ," then the partition function P of two arguments is obtained.)
The such partitions can be enumerated in the Wolfram Language using IntegerPartitions[n, k].
For example, the partitions of 5 of which the largest member is are , , , , and . Similarly, the five partitions of 5 into three or fewer parts are , , , , and .
The satisfy the recurrence relation
with , , and for . The triangle of is given by
(OEIS A026820).