$$U_{681}(x, y) = \frac{\sqrt{\frac{4 x}{\sqrt{1 - 4 y}} + 1}}{2} + \frac{1}{2}$$

$$T_{681}(n, m, k) = \begin{cases}4^{m} {\binom{m + \frac{n}{2} - 1}{m}}&\text{if n = 0} ,\ \\\frac{\left(-1\right)^{n - 1} \cdot 4^{m} k {\binom{- k + 2 n - 1}{n - 1}} {\binom{m + \frac{n}{2} - 1}{m}}}{n} \end{cases} $$