$$U_{502}(x, y) = \frac{\sqrt{1 - 4 y} - 1}{y \left(\frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{2 y^{2}} - 2\right)}$$

$$T_{502}(n, m, k) = \frac{k \left(k + 2 n\right) {\binom{k + n}{n}} {\binom{k + 2 m + 2 n - 1}{m}}}{\left(k + n\right) \left(k + m + 2 n\right)}$$