# polynomial digits of pi

How to find polynomial p_N(n) coefficients a_i_N,

p_N(n) = sum_i ( a_i_N * n^i , i=0:N )

such that p_N(n) gives the decimals of pi (where n=0...N) up to N:th decimal place. I did not find this in Sage ready made.

Does Sage have a function or another way to do this (returning a_i_N for each p_N, N ={1,2,...})? It should be both a numerical value up to a certain precision and a symbolic accurate answer?

This seems like a homework question.