A328122 Number of rooted level-1 phylogenetic networks with n labeled leaves.

1, 3, 36, 723, 20280, 730755, 32171580, 1673573895, 100442870640, 6831585584775, 519288366989700, 43626178967384475, 4014060030471090600, 401443860155706643275, 43359414126089609047500, 5030039291029886037279375, 623762332206315636458124000, 82340968923184527676400655375, 11528273478697179256689693556500

Offset

1,2

Links

Table of n, a(n) for n=1..19.

François Bienvenu, Jean-Jil Duchamps, Michael Fuchs, and Tsan-Cheng Yu, The B_2 index of galled trees, arXiv:2407.19454 [q-bio.PE], 2024. See p. 5.

Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, Maple worksheet

Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, Counting Phylogenetic Networks of level 1 and 2, arXiv:1909.10460 [math.CO], 2019.

Formula

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.

Example

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

Maple

# see links section

Crossrefs

Cf. A328121, A328123, A328126.

Sequence in context: A241996 A366004 A006587 * A091482 A121245 A193754

Adjacent sequences: A328119 A328120 A328121 * A328123 A328124 A328125

Keyword

nonn

Author

Mathilde Bouvel, Oct 04 2019

Status

approved