  New sequences of orthogonal polynomials with respect to the weight functions
$e^{-x} \rho_\nu(x),\ e^{- 1/x} x^{-1} \rho_{\nu} (x), \rho_{\nu}(x)= 2
x^{\nu/2} K_\nu(2\sqrt x),\ x >0, \nu \in \mathbb{R}$, where $K_\nu(z)$ is the
modified Bessel function, are investigated. The recurrence relations, explicit
representations, generating functions and Rodrigues-type formulae are obtained.
