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%I #12 Mar 10 2019 12:40:32
%S 1,1,2,5,14,42,138,462,1663
%N Maximal number of coalescent histories among matching pairs of binary, rooted leaf-labeled gene trees and species trees with n leaves.
%C Consider the unlabeled binary, rooted, leaf-labeled tree topologies with n leaves (A001190). For each unlabeled topology, choose an arbitrary labeling with distinct labels for the n leaves, and assign it to both gene tree and species tree. Compute the number of coalescent histories for that matching (gene tree, species tree) pair according to a recursion (Rosenberg 2007, Theorem 3.1). The sequence a(n) gives the largest number observed among all unlabeled topologies.
%H N. A. Rosenberg, <a href="https://doi.org/10.1089/cmb.2006.0109">Counting coalescent histories</a>, J. Comput. Biol. 14 (2007), 360-377.
%Y Cf. A001190.
%Y A000108 and A005817 give the numbers of coalescent histories for specific families of matching gene trees and species trees.
%K nonn,more
%O 1,3
%A _Noah A Rosenberg_, Feb 14 2019