  One defines a new tree-indexed series, with coefficients that are polynomials
in x over the ring Q(q). Several special evaluations of this series are
obtained, in particular when x is replaced by a q-integer. By taking a limit
value when x = -1/q, one recovers the tree-indexed series Omega_q that was
introduced in a previous article as a q-analog of a classical tree-indexed
series Omega.
