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%I #19 Jan 09 2018 08:33:55
%S 1,1,3,12,66,426,3392,30412,314994,3622332,46379994,648971940,
%T 9923253672,163720448184,2910558776412,55341456735744
%N 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).
%H J. Fulman, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i1r139">Mixing time for a random walk on rooted trees</a>, The Electronic J. of Combinatorics, 16, 2009, R139.
%H M. E. Hoffman, <a href="http://dx.doi.org/10.1090/S0002-9947-03-03317-8 ">Combinatorics of rooted trees and Hopf algebras</a>, Trans. Amer. Math. Soc., 355, 2003, 3795-3811.
%F Apparently, no formula is available. The example gives a hint how the first ten terms of the sequence have been computed (using Maple).
%e 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).
%Y Cf. A206494, A061773.
%K nonn,hard,more
%O 1,3
%A _Emeric Deutsch_, Jul 21 2012
%E a(11)-a(16) from _Alois P. Heinz_, Sep 08 2012
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