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).

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

Offset: 1

Author

Emeric Deutsch, Jul 21 2012

Keywords

• nonn
• hard
• more

Examples

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

Links

• 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, 3795-3811.

Crossrefs

Cf. A206494, A061773.

Formula

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

Extensions

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