I am stuck with the following problem. Every polynomial of degree $d$ can be expressed as $$ p(x) = p_d \binom{x}{d}+ p_{d-1}\binom{x}{d-1} + \cdots + p_0 \binom{x}{0} $$
What is the representation of $$ \binom{x}{i} \binom{x}{j} $$ in such a basis?
I have no idea how to solve this...