Iteration of resolvent operator

I am studying a paper about Markov semigroup and found an equation about resolvent operator. Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a measurable function, and $P(t):\mathcal{M}(\mathbb{R} )\rightarrow \mathcal{M}(\mathbb{R} )$ be a semigroup act on measurable functions. The resolvent operator $R$ is defined by

$Rf \equiv \int_0^{\infty} e^{-t}P(t)fdt$.

The paper mentioned following identity

$R^n f = \int_0^{\infty} \frac{e^{-t} t^n}{n!} P(t)f dt $

without a proof. Could anyone give me some clue or reference about this? Thanks!