This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333006 #13 Apr 01 2020 17:16:32 %S A333006 1,18,1143,120078,17643570,3332111850,769027554540,209740414484160, %T A333006 66001012966991340,23537700706536311400,9381525451337593738800, %U A333006 4132780832455382525556600,1993954501042287608709284400,1045675186072945581517653088800 %N A333006 Number of rooted level-2 phylogenetic networks with n labeled leaves, when multiple (i.e., parallel) edges are not allowed. %H A333006 Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, <a href="http://user.math.uzh.ch/bouvel/publications/BouvelGambetteMansouri_Version2_WithoutMultipleEdges.mw">Maple worksheet</a> %H A333006 Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, <a href="https://arxiv.org/abs/1909.10460">Counting Phylogenetic Networks of level 1 and 2</a>, Version 3, arXiv:1909.10460 [math.CO], 2019. %F A333006 E.g.f. satisfies L(z) = z*f(L(z)) where f(z) = 1 / (1 - (36*z-102*z^2+159*z^3-148*z^4+81*z^5-24*z^6+3*z^7)/(4*(1-z)^6)) [from Bouvel, Gambette, and Mansouri]. - _Sean A. Irvine_, Apr 01 2020 %e A333006 a(3) = 1143 is the number of rooted level-2 phylogenetic networks with 3 labeled leaves. %p A333006 # (See Links) %p A333006 # second Maple program: %p A333006 f:= z-> 1/(1-(36*z-102*z^2+159*z^3-148*z^4+81*z^5-24*z^6+3*z^7) %p A333006 /(4*(1-z)^6)): %p A333006 a:= n-> n!*coeff(series(RootOf(L=z*f(L), L), z, n+1), z, n): %p A333006 seq(a(n), n=1..17); # _Alois P. Heinz_, Apr 01 2020 %Y A333006 Cf. A328121, A328122, A328123, A328126, A333005. %K A333006 nonn %O A333006 1,2 %A A333006 _Mathilde Bouvel_, Mar 13 2020