Variance from pmf recurrence relation

Let $X$ be a random variable having a probability mass function $p(x)$ which is positive only for non-negative integers. If $$p(x+1) = \left(\frac{\ln 3}{x+1}\right) p(x),\quad x=0, 1, 2, \dots,$$ then $\mathrm{Var}(X)$ equals