I'd like to know how to calculate the inverse $z$-transform of $$X(z_{1},z_{2}) = \frac{z_{1}^{-1}}{1 - az_{1}^{-1}z_{2}^{-2}},\quad |z_{1}|\cdot |z_{2}|^{2} > |a|.$$
I`ve tried to make the change $$z_{2}^{2}=t$$ And got $$X(z_{1},t) = \frac{z_{1}^{-1}}{1 - az_{1}^{-1}t^{-1}}, \quad |z_{1}|\cdot |t| > |a|.$$ That brought me to $$x(m,n) = a^{m-1}U(m-1)δ(m-n-1),$$ where I cannot define the second variable n.