$$U_{125}(x, y) = y + \sqrt{4 x y + 1}$$

$$T_{125}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0 and k=0} ,\ \\0&\text{if k=0} ,\ \\4^{n} {\binom{k}{k - m + n}} {\binom{\frac{k}{2} - \frac{m}{2} + \frac{n}{2}}{n}} \end{cases} $$