In this paper we prove results which allow us to enumerate collection of objects of which n1 are identical to each other, another n2 are identical to each other, but different from the first n1, another n3 are identical to each other, but different from any of the first n1+n2,.... These results are used to enumerate forests consisting of n1 isomorphic copies of some tree, n2 isomorphic copies of a different tree,....
Osterweil, Leon J., "A Theorem for Enumerating Certain Types of Collections ; CU-CS-002-72" (1972). Computer Science Technical Reports. 2.