Inverse matrix for $M_{kn}=\frac{i^{(k-n)}}{2^n}\sum_{j=0}^{n} (-1)^j \binom{n}{j}(n-2j)^k$

Question

Good day,

I look for the inverse-matrix formula given the original matrix formula

$$M_{kn}=\frac{i^{(k-n)}}{2^n}\sum_{j=0}^{n} (-1)^j \binom{n}{j}(n-2j)^k,$$

where $M$ is a square matrix with $k,n \le N$. Because $M$ is lower triangular, $M^{-1}$ is also and its elements do not depend on $N$.

Thank you.