$$U_{402}(x, y) = \frac{\left(x + 1\right) \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{2 y^{2}}$$

$$T_{402}(n, m, k) = \frac{k {\binom{k}{n}} {\binom{2 k + 2 m}{m}}}{k + m}$$