Consider a sequence of orthogonal polynomials
$P_0(x) = 1$, $P_1(x) = x$,
and recursively
$P_{n}(x) = (a_n x + b_n) P_{n-1}(x) + c_n P_{n-2}(x)$
for some sequences of real constants $a_n$, $b_n$, $c_n$. What is the representation of $P_n(x)$ in terms of the monomial basis, expressed in the values of $a_n$, $b_n$, $c_n$?