Buckeye leaves are easily recognized because they are palmately compound (leaflets coming from a common point on their petiole or leaf-stalk) and are oppositely arranged on the twig.  Two  species are found in middle Tennessee -- yellow buckeye (Aesculus flava) and Ohio buckeye (Aesculus glabra) -- although neither species is common.  However, yellow buckeye is one of the dominant species in cove forests of the Smoky Mountains.  It is virtually impossible to tell these two species apart on the basis of their leaves and bark alone.  They are best distinguished by their flowers and fruit.  Yellow buckeye flowers are more whitish yellow and have petals with unequal length. Ohio buckeye flowers are more greenish yellow and have petals with equal length.  The fruit of buckeyes is unusual.  Several shiny, brown nuts (poisonous to humans) are present inside a thin hull that splits into several pieces.  The hull of yellow buckeye is smooth, while the hull of Ohio buckeye is spiny.

This tree is described on p. 72 of The Trees of Vanderbilt.