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%I M4232 #27 Dec 14 2019 21:42:10
%S 0,1,1,6,39,390,4815,73080,1304415,26847450,625528575,16279193700,
%T 468022452975,14731683916950,503880434632575,18609309606888000,
%U 738057377647965375,31286068076704691250,1411602439003747365375,67543694966494692445500,3416288904242387117319375
%N Number of planted binary phylogenetic trees with n labels.
%D Foulds, L. R.; Robinson, R. W. Enumeration of binary phylogenetic trees. Combinatorial mathematics, VIII (Geelong, 1980), pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. Math. Rev. 83a:05071.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H L. R. Foulds and R. W. Robinson, <a href="/A006677/a006677.pdf">Enumeration of binary phylogenetic trees</a>, pp. 187-202, Lecture Notes in Math., 884, Springer, Berlin-New York, 1981. (Annotated scanned copy)
%H Plouffe, Simon, <a href="http://arxiv.org/abs/0911.4975">Master's Thesis, Uqam, 1992.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F E.g.f.: -(-1+(1-2*x-2*x^2)^(1/2))/(1+x), Simon Plouffe in his Master's Thesis, Uqam 1992.
%F a(n) ~ sqrt(6-2*sqrt(3)) * (1+sqrt(3))^(n-1) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Oct 01 2013
%t CoefficientList[Series[-(-1+(1-2*x-2*x^2)^(1/2))/(1+x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 01 2013 *)
%K nonn
%O 0,4
%A _N. J. A. Sloane_, _Simon Plouffe_
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