  It is shown that the tridiagonalization of the hypergeometric operator $L$
yields the generic Heun operator $M$. The algebra generated by the operators
$L,M$ and $Z=[L,M]$ is quadratic and a one-parameter generalization of the
Racah algebra. The new Racah-Heun orthogonal polynomials are introduced as
overlap coefficients between the eigenfunctions of the operators $L$ and $M$.
An interpretation in terms of the Racah problem for $su(1,1)$ algebras and
separation of variables in a superintegrable system are discussed.
