Let $n\in Z^+$ and $poly(n)$ be a polynomial with domain $Z^+$. Then what are the necessary and sufficient conditions in regards to the coefficients of $poly(n)$ for the following to hold?
$poly(n):Z^+\rightarrow Z$
Is it simply that the coefficients are integers? Or are there, for example, polynomials with some non-integer rational coefficients that always produce an integer?