A328121 Number of unrooted level-1 phylogenetic networks (also called galled trees) with (n+1) labeled leaves.

1, 2, 15, 192, 3450, 79740, 2252880, 75227040, 2898481320, 126570502800, 6177380517000, 333231084648000, 19687828831070400, 1264341183311606400, 87691200344603856000, 6532556443068591936000, 520205544912884502672000, 44098092640676115673632000, 3964782594938523231457584000

Offset

1,2

Links

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

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.

Charles Semple and Mike Steel, Unicyclic networks: compatibility and enumeration, Transactions on Computational Biology and Bioinformatics (3:1 pp.398--401), 2006.

Formula

Semple and Steele provide a summation formula for a(n) (see their Theorem 4).

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.

Example

a(4) = 192 is the number of unrooted level-1 phylogenetic networks with 5 labeled leaves

Maple

# see links section

Crossrefs

Cf. A328122, A328123, A328126, A333005, A333006.

Sequence in context: A098343 A052819 A349292 * A127090 A198522 A187655

Adjacent sequences: A328118 A328119 A328120 * A328122 A328123 A328124

Keyword

nonn

Author

Mathilde Bouvel, Oct 04 2019

Status

approved