Planted Tree
02:44 AM
22-5-2022
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A planted tree is a rooted tree whose root vertex has vertex degree 1. The number of planted trees of 
nodes is 
, where 
is the number of rooted trees of 
vertices (Harary 1994, pp. 188-190), so there are 0, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, ... (OEIS A000081) planted trees of 
, 2, 3, ... vertices.
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.
Sloane, N. J. A. Sequence A000081/M1180 in "The On-Line Encyclopedia of Integer Sequences."
