  We introduce orthogonal polynomials $M_j^{\mu,\ell}(x)$ as eigenfunctions of
a certain self-adjoint fourth order differential operator depending on two
parameters $\mu\in\mathbb{C}$ and $\ell\in\mathbb{N}_0$.
  These polynomials arise as $K$-finite vectors in the $L^2$-model of the
minimal unitary representations of indefinite orthogonal groups, and reduce to
the classical Laguerre polynomials $L_j^\mu(x)$ for $\ell=0$.
  We establish various recurrence relations and integral representations for
our polynomials, as well as a closed formula for the $L^2$-norm. Further we
show that they are uniquely determined as polynomial eigenfunctions.
