Explicit form of the Yablonskii - Vorob'ev polynomials
  Special polynomials associated with rational solutions of the second Painlev\'{e} equation and other members of its hierarchy are discussed. New approach, which allows one to construct each polynomial is presented. The structure of the polynomials is established. Formulas of their coefficients are found. Correlations between the roots of every polynomial are obtained. 
Maria V. Demina, Nikolai A. Kudryashov