The authors discuss the relationship between the theory of fourth Painlevé equation \[ \frac{{{d}^{2}}q}{d{{z}^{2}}}=\frac{1}{2q}{{\left( \frac{dq}{dz} \right)}^{2}}+\frac{3}{2}{{q}^{3}}+4z{{q}^{2}}+2({{z}^{2}}-A)q+\frac{B}{q} \tag{1} \] and the theory of orthogonal polynomials with respect to a semiclassical Laguerre weight \[ \omega (x;t)={{x}^{\lambda }}\exp (-{{x}^{2}}+tx),x\in \mathbb{R}. \] For quite a wide variety of parameters the solutions of equation (1) lie in the Picard-Vessiot extension of the field \(\mathbb{C}(z)\) and can be expressed in terms of classical special functions. The semiclassical orthogonal polynomials satisfy a three-term recurrence relationship of the form \[ x{{P}_{n}}(x;t)={{P}_{n+1}}(x;t)+{{\alpha }_{n}}(t){{P}_{n}}(x;t)+{{\beta }_{n}}(t){{P}_{n-1}}(x;t), \tag{2} \] where the coefficients \({\alpha _n}(t)\) and \({\beta _n}(t)\) also can be expressed in terms of classical special functions. This allows the authors to obtain an expression for the coefficients of relation (2) through solutions of the Painlevé equation \[ \begin{aligned} &{\alpha }_{n}(t)=\frac{1}{2}{{q}_{n}}(t)+\frac{1}{2}t, \\ &{\beta }_{n}(t)=-\frac{1}{8}\frac{d{{q}_{n}}}{dt}-\frac{1}{8}q_{n}^{2}-\frac{1}{4}t{{q}_{n}}+\frac{1}{4}\lambda +\frac{1}{2}, \end{aligned} \] where \({{q}_{n}}(z)\) is a solution of equation (1) with parameters \((A,B)=(2n+\lambda +1,-2{{\lambda }^{2}})\).