I am studying some classes of orthogonal polynomials and want to find out which of them belong to the Askey scheme. To give a simple example consider the polynomials $${p_n}(x,r) = \sum\limits_{k = 0}^{\left\lfloor {\frac{n}{2}} \right\rfloor } {{{( - 1)}^k}c(n,k,r){x^{n - 2k}}} $$ with $$c(n,k,r) = \binom{\lfloor{{n}/2}\rfloor}k \prod\limits_{j = 0}^{k - 1} {\left( {\left\lfloor {\frac{{n + 1 - 2j}}{2}} \right\rfloor r - 1} \right)}.$$ For $r = 2$ they coincide with the (probabilists’) Hermite polynomials.
My questions are: Have these polynomials been studied in the literature? Which of them belong to the Askey scheme?