I believe you mean "describable by a polynomial formula", in which case the answer is "yes".

Given n terms s\sb 0, \cdots, s\sb {n-1} http://latex.mathoverflow.net/png?s%5F0%2C%20%5Ccdots%2C%20s%5F%7Bn%2D1%7D, start with a polynomial of degree n:

a\sb 1x^n+a\sb 2x^{n-1}+ \cdots + a\sb {n-1}x + a\sb n http://latex.mathoverflow.net/png?a%5F1x%5En%2Ba%5F2x%5E%7Bn%2D1%7D%2B%20%5Ccdots%20%2B%20a%5F%7Bn%2D1%7Dx%20%2B%20a%5Fn

Create a system of n equations such that for each polynomial where x = 0, .. , n-1 the polynomial is set equal to s\sb 0, \cdots, s\sb {n-1} http://latex.mathoverflow.net/png?s%5F0%2C%20%5Ccdots%2C%20s%5F%7Bn%2D1%7D.

Solve the system of equations for all terms a\sb 1, \cdots, a\sb n http://latex.mathoverflow.net/png?a%5F1%2C%20%5Ccdots%2C%20a%5Fn and voila, a formula.

Now repeat the same thing for a polynomial of one higher degree, dropping the a\sb {n-1}x http://latex.mathoverflow.net/png?a%5F%7Bn%2D1%7Dx term so there are still n terms in total.

Voila, a second formula.

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.