I apologize if this is too elementary. The following identity arises in cluster algebra, where I'm trying to find an expression for cluster variables. Let $a,b$ be any nonnegative integers. Then there are nonnegative integers $d_0,...,d_{a+b}$ (depending on $a,b$, but not $X$) such that $$ {X\choose a} {X\choose b} = \sum_{i=0}^{a+b} d_i{X\choose i} $$for all large enough integers $X\gg 0$. I could prove this, but I'm pretty sure this must be well-known. I just want to get a reference. Or very short proofs (less than five lines) are welcome, too. Thank you.