

A214565


Sum(M(t)), where summation is over all rooted trees t with n vertices and M(t) is the number of ways to take apart t by sequentially removing terminal edges (see A206494).


0



1, 1, 3, 12, 66, 426, 3392, 30412, 314994, 3622332, 46379994, 648971940, 9923253672, 163720448184, 2910558776412, 55341456735744
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..16.
J. Fulman, Mixing time for a random walk on rooted trees, The Electronic J. of Combinatorics, 16, 2009, R139.
M. E. Hoffman, Combinatorics of rooted trees and Hopf algebras, Trans. Amer. Math. Soc., 355, 2003, 37953811.


FORMULA

Apparently, no formula is available. The example gives a hint how the first ten terms of the sequence have been computed (using Maple).


EXAMPLE

a(4) = 12 because there are four rooted trees with 4 vertices; their MatulaGoebel numbers are 5,6,7, and 8 and, consequently M(5)+M(6)+M(7)+M(8) = 1+3+2+6 = 12 (see A206494).


CROSSREFS

Cf. A206494, A061773.
Sequence in context: A074513 A290147 A007871 * A267323 A058790 A199746
Adjacent sequences: A214562 A214563 A214564 * A214566 A214567 A214568


KEYWORD

nonn,hard,more


AUTHOR

Emeric Deutsch, Jul 21 2012


EXTENSIONS

a(11)a(16) from Alois P. Heinz, Sep 08 2012


STATUS

approved



