$$U_{501}(x, y) = \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}} + \frac{1 - \sqrt{1 - 4 y}}{2 y}$$

$$T_{501}(n, m, k) = \frac{\left(k + n\right) {\binom{k}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$