Discuss the recurrence of such a Markov chain

Question

$\{X_n:n\ge0\}$ is a Markov chain in $\{0,1,2,\ldots\}$ whose transition probability satisfy $p_{01}=1, p_{i,i+1}+p_{i,i-1}=1$ and $$ p_{i,i+1}=(\frac{i+1}{i})^\alpha p_{i,i-1}, i\ge1,\alpha\in(0,\infty) $$ then discuss the recurrence of the Markov chain.