Geodesic
A counting formula for labeled, rooted forests
Journal of Algebraic Combinatorics, Tome 15 (2002) no. 1, pp. 71-97.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Given a power series, the coefficients of the formal inverse may be expressed as polynomials in the coefficients of the original series. Further, these polynomials may be parameterized by certain ordered, labeled forests. There is a known formula for the formal inverse, which indirectly counts these classes of forests, developed in a non-direct manner. Here, we provide a constructive proof for this counting formula that explains why it gives the correct count. Specifically, we develop algorithms for building the forests, enabling us to count them in a direct manner.
Keywords: trees, forests, counting formula, polynomials, reversion 
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Lampe, Kristen A. A counting formula for labeled, rooted forests. Journal of Algebraic Combinatorics, Tome 15 (2002) no. 1, pp. 71-97. http://geodesic.mathdoc.fr/item/JAC_2002__15_1_a0/