$$U_{854}(x, y) = \frac{- 2 x y^{2} + 4 x y - 2 x - \sqrt{4 x y^{2} - 8 x y + 4 x + 1} - 1}{2 y^{3} - 6 y^{2} + 6 y - 2}$$

$$T_{854}(n, m, k) = \begin{cases}{\binom{3 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}} {\binom{3 k + m - 2 n - 1}{m}}}{n} \end{cases} $$