A136719 Number of labeled directed trees with n nodes.

1, 3, 27, 432, 10125, 314928, 12252303, 573308928, 31381059609, 1968300000000, 139234453205859, 10968475320188928, 952427511967417317, 90388408459919044608, 9308590679915771484375, 1033947715493982426365952, 123217926482311669202664753, 15682720840457750419215679488

Offset: 1

Author

Christian G. Bower, Jan 18 2008

Keywords

• nonn

Comments

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

References

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for sequences related to trees

Crossrefs

Cf. A006965 (unlabeled version).

Programs

PARI

seq(n)={Vec(serlaplace((-1/3)*lambertw(-3*x + O(x*x^n))/x))} \\ Andrew Howroyd, Feb 02 2020

PARI

a(n) = {3*(3*n)^(n-2)} \\ Andrew Howroyd, Feb 02 2020

Formula

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

a(n) = 3*(3*n)^(n-2). - Andrew Howroyd, Feb 02 2020

Extensions

Terms a(16) and beyond from Andrew Howroyd, Feb 02 2020