$$U_{852}(x, y) = \frac{- 2 x y + 2 x + \sqrt{- 4 x y + 4 x + 1} + 1}{2 y^{2} - 4 y + 2}$$

$$T_{852}(n, m, k) = \begin{cases}1&\text{if n=0, m=0} ,\ \\\frac{2 \left(-1\right)^{m + n - 1} k {\binom{m + n}{n}} {\binom{- 2 k + 2 n - 1}{m + n - 1}}}{m + n} \end{cases} $$