  We discuss the relationship between the recurrence coefficients of orthogonal
polynomials with respect to a generalized Freud weight
\[w(x;t)=|x|^{2\lambda+1}\exp\left(-x^4+tx^2\right),\qquad x\in\mathbb{R},\]
with parameters $\lambda>-1$ and $t\in\mathbb{R}$, and classical solutions of
the fourth Painlev\'{e} equation. We show that the coefficients in these
recurrence relations can be expressed in terms of Wronskians of parabolic
cylinder functions that arise in the description of special function solutions
of the fourth Painlev\'{e} equation. Further we derive a second-order linear
ordinary differential equation and a differential-difference equation satisfied
by the generalized Freud polynomials.
