I wrote in response to Rich's post: << The only thing I notice worth mentioning is that (clearly) in counting the partitions of a multiset, the count depends only on the "shape" of the multiset, and such shapes are in one-to-one correspondence with the set of integer partitions. So this defines an interesting function from the set of integer partitions to the integers.
Another potentially interesting function here goes from integers to multisets. Given any integer N, one has its set of partitions, P(N). For each partition p in P(N), let K(p) be the number of partitions of [a multiset having shape p]. Then the set M(N) := { K(p) : p is in P(N) } is a multiset (of integers) depending on N. Going yet farther, M(N) has a shape which is an integer partition, say part(N). This defines a function taking the integer N to the integer partiion part(N). --Dan