Definition 10.57.3. Let $A$ be an abelian group. We say that a function $f : n \mapsto f(n) \in A$ defined for all sufficient large integers $n$ is a *numerical polynomial* if there exists $r \geq 0$, elements $a_0, \ldots , a_ r\in A$ such that

\[ f(n) = \sum \nolimits _{i = 0}^ r \binom {n}{i} a_ i \]

for all $n \gg 0$.

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