Hello,

while dealing with nonhomogeneous equations with constant coefficients I ecountered a following problem - I need to calculate powers of a given matrix (all powers up to n-1):

$\displaystyle \mathbb N^{n}_{n} \ni \mathbb M_{n}= \begin{bmatrix} 0&n-1&0&0&...&0&0&0&0\\0&0&n-2&0&...&0&0&0&0\\0&0&0&n-3&...&0&0&0&0\\...&...&...&...&...&...&...&...&... \\0&0&0&0&...&0&3&0&0\\0&0&0&0&...&0&0&2&0\\0&0&0& 0&...&0&0&0&1\\0&0&0&0&...&0&0&0&0 \end{bmatrix}$

Is there an easy way to calculate it?