$$U_{114}(x, y) = \frac{- y - \sqrt{x \left(4 y - 4\right) + y^{2} - 2 y + 1} + 1}{2 x}$$

$$T_{114}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{m + n}{n}} {\binom{k + 2 n - 1}{k + n}}}{m + n} \end{cases} $$