Planted Tree

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.

REFERENCES

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.

Sloane, N. J. A. Sequence A000081/M1180 in "The On-Line Encyclopedia of Integer Sequences."