Consider the monic orthogonal polynomials determined by the recurrence $$p_{n+1}(x)=(x-n(n+b))p_{n}(x)-n(n+a)p_{n-1}(x), \quad n\in\mathbb{N},$$ with the initial conditions $p_{-1}(x)=0$ and $p_{0}(x)=1$. The parameters $a$ and $b$ are assumed to be $a>-1$ and $b\in\mathbb{R}$. I am particularly interested in the following questions:

1) Is their measure of ortogonality expressible in terms of some special functions?

2) Is there a generating function for this family expressible in terms of some special functions?

**Remark:** Let me remark that I've checked the Askey scheme but found nothing. There are several polynomials in the Askey scheme whose coefficients from the three-term recurrence are polynomials in $n$ of low degree. These coefficients sometimes look similarly as above but it seems that they are never both quadratic in $n$.