$$U_{256}(x, y) = y + \frac{1 - \sqrt{1 - 4 x}}{2 x}$$

$$T_{256}(n, m, k) = \begin{cases}0&\text{if k<m} ,\ \\{\binom{k}{m}}&\text{if n=0} ,\ \\\frac{\left(k - m\right) {\binom{k}{m}} {\binom{k - m + 2 n - 1}{n}}}{k - m + n}&\text{if n>0} \end{cases} $$