$$U_{122}(x, y) = \frac{1}{\sqrt{1 - 4 x} \sqrt{1 - 4 y}}$$

$$T_{122}(n, m, k) = 4^{m + n} {\binom{\frac{k}{2} + m - 1}{m}} {\binom{\frac{k}{2} + n - 1}{n}}$$