If $S_n=T*f_n$ and $T$ is a $C_0$-semigroup then the corresponding generator $A$ is determined by \[ Ax=(n+1)!im_{h\downarrow0}\frac{S-n(h)x-\frac{h^n}{n!}x}{h^{n+1}}, \quad xı D(A). \] The same holds for a general $n$-times integrated exponentially bounded .