A136796 Number of labeled marked rooted trees with n nodes.

2, 16, 288, 8192, 320000, 15925248, 963780608, 68719476736, 5642219814912, 524288000000000, 54394721876836352, 6232805962420322304, 781754012972500385792, 106530593546206374264832, 15672832819200000000000000, 2475880078570760549798248448

Offset: 1

Author

Christian G. Bower, Jan 21 2008

Keywords

• nonn

Comments

A marked rooted tree is a rooted tree where each node and edge is marked as + or -.

References

• F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 293 (4.1.60).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A136794 (unlabeled version), A136797 (tree version).

Programs

Magma

[2^(2*n-1)*n^(n-1): n in [1..20]]; // Vincenzo Librandi, Mar 29 2014

Mathematica

Table[2^(2*n-1)*n^(n-1),{n,1,20}] (* Vaclav Kotesovec, Mar 29 2014 *)

Formula

E.g.f.: B(4*x)/2 where B(x) is e.g.f. of A000169.

a(n) = A052764(n)*2.

a(n) = 2^(2*n-1) * n^(n-1). - Vaclav Kotesovec, Mar 29 2014

Extensions

More terms from Vincenzo Librandi, Mar 29 2014