  We construct a set $H$ of orthogonal polynomial sequences that contains all
the families in the Askey scheme and the $q$-Askey scheme. The polynomial
sequences in $H$ are solutions of a generalized first-order difference equation
which is determined by three linearly recurrent sequences of numbers. Two of
these sequences are solutions of a difference equation of order three and the
other sequence satisfies a related difference equation of order five.
  We obtain explicit expressions for the coefficients of the orthogonal
polynomials and for the generalized moments with respect to a basis of Newton
type of the space of polynomials. We also obtain explicit formulas for the
coefficients of the three-term recurrence relation satisfied by the polynomial
sequences in $H$.
  The set $H$ contains all the 15 families in the Askey scheme and all the 29
families in the $q$-Askey scheme. Each of these families is obtained by direct
substitution of appropriate values for the parameters in our general formulas.
The only cases that require some limits are the Hermite and continuous
$q$-Hermite polynomials. We present the values of the parameters for some of
the families.
