A328126 Number of rooted level-2 phylogenetic networks with n labeled leaves, when multiple (i.e. parallel) edges are allowed.

1, 24, 1935, 259098, 48547410, 11693494530, 3442245242940, 1197493950509640, 480665307600153900, 218657025956206794600, 111169169621733787779600, 62469471023839610046855000, 38446561750101105716524609200, 25719207873623040944564642044800, 18581469164514130166868945471102000

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, Maple worksheet

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

Formula

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.

Example

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

Maple

# see links section

Crossrefs

Cf. A328121, A328122, A328123.

Sequence in context: A003738 A006685 A002671 * A225220 A262010 A267075

Adjacent sequences: A328123 A328124 A328125 * A328127 A328128 A328129

Keyword

nonn

Author

Mathilde Bouvel, Oct 04 2019

Extensions

Name clarified by Mathilde Bouvel, Feb 03 2020

Status

approved