  It is shown that the monomials $\Lambda=(z^n)_{n=0}^{\infty}$ are a Schauder
basis of the Fr\'echet spaces $A_+^{-\gamma}, \ \gamma \geq 0,$ that consists
of all the analytic functions $f$ on the unit disc such that
$(1-|z|)^{\mu}|f(z)|$ is bounded for all $\mu > \gamma$. Lusky \cite{L} proved
that $\Lambda$ is not a Schauder basis for the closure of the polynomials in
weighted Banach spaces of analytic functions of type $H^{\infty}$. A sequence
space representation of the Fr\'echet space $A_+^{-\gamma}$ is presented. The
case of (LB)-spaces $A_{-}^{-\gamma}, \ \gamma > 0,$ that are defined as unions
of weighted Banach spaces is also studied.
