I believe you mean "describable by a polynomial formula", in which case the answer is "yes".
Given $n$ terms $s_0, \cdots, s_{n-1}$, start with a polynomial of degree $n$:
$$a_1x^n+a_2x^{n-1}+ \cdots + a_{n-1}x + a_n$$
Create a system of $n$ equations such that for each polynomial where $x = 0, \ldots , n-1$ the polynomial is set equal to $s_0, \cdots, s_{n-1}$.
Solve the system of equations for all terms $a_1, \cdots, a_n$ and voila, a formula.
Now repeat the same thing for a polynomial of one higher degree, dropping the $a_{n-1}x$ term so there are still $n$ terms in total.
Voila, a second formula.
