$$U_{878}(x, y) = \frac{- 2 x \sqrt{4 y + 1} - \sqrt{- 4 x \sqrt{4 y + 1} + 1} + 1}{2 x^{2} \left(4 y + 1\right)}$$

$$T_{878}(n, m, k) = \begin{cases}1&\text{if n=0,m=0, k=0} ,\ \\\frac{4^{m} k {\binom{k + 3 n - 1}{n}} {\binom{\frac{k}{2} + 2 m + n - 1}{m}}}{k + 2 m + 2 n}&\text{if k even} ,\ \\\frac{k {\binom{k + 3 n - 1}{n}} {\binom{\frac{k}{2} + 2 m + n - \frac{1}{2}}{m}} {\binom{k + 4 m + 2 n - 1}{\frac{k}{2} + 2 m + n - \frac{1}{2}}}}{\left(k + 2 m + 2 n\right) {\binom{k + 2 m + 2 n - 1}{\frac{k}{2} + m + n - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$