  Special polynomials associated with rational solutions of the second
Painlev'e equation and other equations of its hierarchy are studied. A new
method, which allows one to construct each family of polynomials is presented.
The structure of the polynomials is established. Formulaes for their
coefficients are found. The degree of every polynomial is obtained. The main
achievement of the method lies in the fact that it enables one to construct the
family of polynomials corresponding to any member of the second Painlev'e
hierarchy. Our approach can be applied for deriving the polynomials related to
rational or algebraic solutions of other nonlinear differential equations.
