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%I #22 Apr 05 2020 04:23:44
%S 1,2,15,192,3450,79740,2252880,75227040,2898481320,126570502800,
%T 6177380517000,333231084648000,19687828831070400,1264341183311606400,
%U 87691200344603856000,6532556443068591936000,520205544912884502672000,44098092640676115673632000,3964782594938523231457584000
%N Number of unrooted level-1 phylogenetic networks (also called galled trees) with (n+1) labeled leaves.
%H Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, <a href="http://user.math.uzh.ch/bouvel/publications/BouvelGambetteMansouri.mw">Maple worksheet</a>
%H Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, <a href="https://arxiv.org/abs/1909.10460">Counting Phylogenetic Networks of level 1 and 2</a>, arXiv:1909.10460 [math.CO], 2019.
%H Charles Semple and Mike Steel, <a href="https://doi.org/10.1109/TCBB.2006.14">Unicyclic networks: compatibility and enumeration</a>, Transactions on Computational Biology and Bioinformatics (3:1 pp.398--401), 2006.
%F Semple and Steele provide a summation formula for a(n) (see their Theorem 4).
%F Bouvel, Gambette and Mansouri provide (among other additional results) an equation for the associated exponential generating function, and an asymptotic estimate of a(n). See their Section 4.
%e a(4) = 192 is the number of unrooted level-1 phylogenetic networks with 5 labeled leaves
%p # see links section
%Y Cf. A328122, A328123, A328126, A333005, A333006.
%K nonn
%O 1,2
%A _Mathilde Bouvel_, Oct 04 2019
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