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A214565
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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).
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0
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1, 1, 3, 12, 66, 426, 3392, 30412, 314994, 3622332, 46379994, 648971940, 9923253672, 163720448184, 2910558776412, 55341456735744
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OFFSET
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1,3
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LINKS
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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, 3795-3811.
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FORMULA
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Apparently, no formula is available. The example gives a hint how the first ten terms of the sequence have been computed (using Maple).
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EXAMPLE
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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).
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CROSSREFS
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Cf. A206494, A061773.
Sequence in context: A074513 A290147 A007871 * A267323 A058790 A199746
Adjacent sequences: A214562 A214563 A214564 * A214566 A214567 A214568
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KEYWORD
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nonn,hard,more
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AUTHOR
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Emeric Deutsch, Jul 21 2012
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EXTENSIONS
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a(11)-a(16) from Alois P. Heinz, Sep 08 2012
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STATUS
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approved
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