  We show generic existence of power series a with complex coefficients a_n,
such that the sequence of partial sums of a new power series where its
coefficients b_n are functions of a_0, a_1, ..., a_n approximate every
polynomial uniformly on every compact set K not containing the origin and with
connected complement. The functions b_n are assumed to be continuous and such
that for every complex numbers a_0, a_1, ... , a_{n - 1}, c there exists a
complex number a_n such that b_n(a_0, a_1,..., a_{n-1}, a_n) = c. This clearly
covers the case of linear functions b_n.
