  Under certain constraints on the parameters a, b and c, it is known that
Schroedinger's equation
  -y"(x)+(ax^6+bx^4+cx^2)y(x) = E y(x), a > 0, with the sextic anharmonic
oscillator potential is exactly solvable. In this article we show that the
exact wave function y is the generating function for a set of orthogonal
polynomials P_n^{(t)}(x) in the energy variable E. Some of the properties of
these polynomials are discussed in detail and our analysis reveals scaling and
factorization properties that are central to quasi-exact solvability. We also
prove that this set of orthogonal polynomials can be reduced,by means of a
simple scaling transformation, to a remarkable class of orthogonal polynomials,
P_n(E)=P_n^{(0)}(E) recently discovered by Bender and Dunne.
