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A328122 Number of rooted level-1 phylogenetic networks with n labeled leaves. 5
1, 3, 36, 723, 20280, 730755, 32171580, 1673573895, 100442870640, 6831585584775, 519288366989700, 43626178967384475, 4014060030471090600, 401443860155706643275, 43359414126089609047500, 5030039291029886037279375, 623762332206315636458124000, 82340968923184527676400655375, 11528273478697179256689693556500 (list; graph; refs; listen; history; text; internal format)
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.

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: A224184 A241996 A006587 * A091482 A121245 A193754

Adjacent sequences:  A328119 A328120 A328121 * A328123 A328124 A328125

KEYWORD

nonn

AUTHOR

Mathilde Bouvel, Oct 04 2019

STATUS

approved

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Last modified August 14 13:43 EDT 2022. Contains 356117 sequences. (Running on oeis4.)