Find the stationary distribution of the following Markov chain

Question

Suppose Markov chain $\{X_{n},n\geq 1\}$ with space $I=\{0,1,2,...\}$ and $$p_{i j}=e^{-\lambda} \sum_{k=0}^{i \wedge j} C_{i}^{k}(1-q)^{k} q^{i-k} \frac{\lambda^{j-k}}{(j-k) !}$$ where $i\wedge j=min\{i,j\}$ and $\lambda>0,0<q<1$ are constants. Please show that $$\lim _{n \rightarrow \infty} p_{i j}^{(n)}=\frac{1}{j !} e^{-\frac{\lambda}{q}}\left(\frac{\lambda}{q}\right)^{j}$$