$$U_{259}(x, y) = x + \frac{- 2 y - \sqrt{1 - 4 y} + 1}{2 y^{2}}$$

$$T_{259}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{2 k {\binom{k - 1}{n}} {\binom{2 k + 2 m - 2 n - 1}{m - 1}}}{m} \end{cases} $$