$$U_{445}(x, y) = x + \frac{\sqrt{\frac{4 x}{1 - y} + \frac{1}{\left(1 - y\right)^{2}}}}{2} + \frac{1}{2 - 2 y}$$

$$T_{445}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if n>0 and m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + n - 1}{m - 1}} {\binom{2 k - n - 1}{n}}}{m} \end{cases} $$