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. Extension to the enumeration formula in the

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... hronous genealogy with m samples of total size n = n1 + · · · + nm yields a non-recursive nested sum-product. These enumeration formulae measure sample spaces of Bayesian prior distributions of trees relevant to theoretical and computational phylogenetics.