$$U_{307}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right) \left(1 - \sqrt{1 - 4 y}\right)}{4 x y}$$

$$T_{307}(n, m, k) = \frac{k^{2} {\binom{k + 2 m - 1}{m}} {\binom{k + 2 n - 1}{n}}}{\left(k + m\right) \left(k + n\right)}$$