I am reading both the papers on one-of-many proofs (mainly this one: https://eprint.iacr.org/2014/764.pdf) and trying to implement the protocol as in section 3 (see figure 2).

The paper specifies computing the polynomial coefficients p_i_k, but I cannot find any explanation for how those coefficients are to be calculated. Can anyone help me understand this?

Look at the line above the equation (1) on page 9. For each i \in {0,...N-1}, the polynomial P_i(X) = \prod_{j=1}^n f_{j, i_j}. So you can compute each polynomal after constructing the f_i_j matrix as is described in the paper