Non-Recursive Enumeration of Heterochronous Trees

The enumeration formula of a non-contemporaneous genealogy with total sample size n = n1 + n2 requires a nested sum-product. The set of ancestral patterns in the noncontemporaneous genealogy yields a multiplicity factor that translates from the set of ancestral patterns in the isochronous genealogy. A computation formula of the multiplicity factor proves to be non-recursive. Evaluation of small sample sizes demonstrates the emergent complexity.