$$U_{316}(x, y) = \frac{1 - \sqrt{1 - 4 x}}{2 x \left(1 - y\right)^{2}}$$

$$T_{316}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{2 k + m - 1}{m}}}{k + n}$$