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We can now express the coeficcients of a generating function's polynomial directly for example \begin{equation}  G_4=\frac{-17z^3+34z^2-26z+7}{(z-1)^4} G_4=\frac{-17z^3+34z^2-26z+7}{(z-1)^4}=\frac{M_{44}z^3+M_{43}z^2+M_{42}z+M_{41}}{(z-1)^4}  \end{equation}