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Number of rooted level-2 phylogenetic networks with n labeled leaves, when multiple (i.e. parallel) edges are allowed.
5

%I #12 Feb 03 2020 05:55:52

%S 1,24,1935,259098,48547410,11693494530,3442245242940,1197493950509640,

%T 480665307600153900,218657025956206794600,111169169621733787779600,

%U 62469471023839610046855000,38446561750101105716524609200,25719207873623040944564642044800,18581469164514130166868945471102000

%N Number of rooted level-2 phylogenetic networks with n labeled leaves, when multiple (i.e. parallel) edges are allowed.

%H Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, <a href="http://user.math.uzh.ch/bouvel/publications/BouvelGambetteMansouri_Version1_WithMultipleEdges.mw">Maple worksheet</a>

%H Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, <a href="https://arxiv.org/abs/1909.10460v2">Counting Phylogenetic Networks of level 1 and 2</a>, Version 2, arXiv:1909.10460 [math.CO], 2019.

%F Bouvel, Gambette and Mansouri provide (among other results) a closed formula for a(n), an equation for the associated exponential generating function, and an asymptotic estimate of a(n). See their Section 7.

%e a(3) = 1935 is the number of rooted level-2 phylogenetic networks with 3 labeled leaves.

%p # see links section

%Y Cf. A328121, A328122, A328123.

%K nonn

%O 1,2

%A _Mathilde Bouvel_, Oct 04 2019

%E Name clarified by _Mathilde Bouvel_, Feb 03 2020