  We construct W-algebra generalizations of the ^sl(2) algebra -- W-algebras
W^{(2)}_n generated by two currents E and F with the highest pole of order n in
their OPE. The n=3 term in this series is the Bershadsky--Polyakov algebra. We
define these algebras as a centralizer (commutant) of the $U_{q}sl(n|1)$ super
quantum group and explicitly find the generators in a factored, ``Miura-like''
form. Another construction of W^{(2)}_n is in terms of the coset
^sl(n|1)/^sl(n). The relation between the two constructions involves the
``duality'' (k+n-1)(k'+n-1)=1 between levels k and k' of two ^sl(n) algebras.
