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Number of labeled directed trees with n nodes.
2

%I #12 Feb 02 2020 17:41:01

%S 1,3,27,432,10125,314928,12252303,573308928,31381059609,1968300000000,

%T 139234453205859,10968475320188928,952427511967417317,

%U 90388408459919044608,9308590679915771484375,1033947715493982426365952,123217926482311669202664753,15682720840457750419215679488

%N Number of labeled directed trees with n nodes.

%C A directed tree is a tree where each edge is assigned one or both directions.

%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 292 (4.1.58).

%H Andrew Howroyd, <a href="/A136719/b136719.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(n) = A052756(n)/n.

%F a(n) = 3*(3*n)^(n-2). - _Andrew Howroyd_, Feb 02 2020

%o (PARI) seq(n)={Vec(serlaplace((-1/3)*lambertw(-3*x + O(x*x^n))/x))} \\ _Andrew Howroyd_, Feb 02 2020

%o (PARI) a(n) = {3*(3*n)^(n-2)} \\ _Andrew Howroyd_, Feb 02 2020

%Y Cf. A006965 (unlabeled version).

%K nonn

%O 1,2

%A _Christian G. Bower_, Jan 18 2008

%E Terms a(16) and beyond from _Andrew Howroyd_, Feb 02 2020