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In direct as well as diagonal reversion of a system of power series, the reversion coecients may be expressed as polynomials in the coecients of the original power series. These polynomials have coecients which are natural numbers (Raney coecients). We provide a combinatorial interpretation for Raney coecients. Specically, each such coecient counts a certain collection of ordered colored trees. We also provide a simple determinantal formula for Raney coecients which involves multinomial coecients.

Reversion of power series and the extended Raney coefficients