# Write the command for this recursive formula?

GROUPS:
 Hey guys:I have following recursive formula: $\mathbb{E}[Z_t^n]=\sum_{k=0}^{n-1}\binom{n}{k}\mathbb{E}[X^{n-k} ][\int_0^t e^{-n \delta v} \mathbb{E}[Z_{t-v}^k] dm(v)]$where $\mathbb{E}$ is the expectation of random variable. You may assume X is exponential distributed and $m(t)=\lambda t, \lambda>0$. Further, $\mathbb{E}[Z_t^0]=1$.I am wondering how can I write the commands to achieve $\mathbb{E}[Z_t^n]$ for n large, no matter numerically or theoretically.Thanks in advance.