A328122 - OEIS

%I #18 Aug 08 2024 11:05:29

%S 1,3,36,723,20280,730755,32171580,1673573895,100442870640,

%T 6831585584775,519288366989700,43626178967384475,4014060030471090600,

%U 401443860155706643275,43359414126089609047500,5030039291029886037279375,623762332206315636458124000,82340968923184527676400655375,11528273478697179256689693556500

%N Number of rooted level-1 phylogenetic networks with n labeled leaves.

%H François Bienvenu, Jean-Jil Duchamps, Michael Fuchs, and Tsan-Cheng Yu, <a href="https://arxiv.org/abs/2407.19454">The B_2 index of galled trees</a>, arXiv:2407.19454 [q-bio.PE], 2024. See p. 5.

%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.

%F Bouvel, Gambette and Mansouri provide (among other results) a closed formula for a(n), an equation and a closed form for the associated exponential generating function, and an asymptotic estimate of a(n). See their Section 5.

%e a(4) = 723 is the number of rooted level-1 phylogenetic networks with 4 labeled leaves.

%p # see links section

%Y Cf. A328121, A328123, A328126.

%K nonn

%O 1,2

%A _Mathilde Bouvel_, Oct 04 2019