  We present new functional equations for the species of plane and of planar
(in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed
species. We then deduce the explicit molecular expansion of these species, i.e
a classification of their structures according to their stabilizers. There
result explicit formulas in terms of Catalan numbers for their associated
generating series, including the asymmetry index series. This work is closely
related to the enumeration of polyene hydrocarbons of molecular formula
C_nH_n+2.
