$$U_{131}(x, y) = \frac{- 2 x y - 2 x - \sqrt{1 - 4 x} \sqrt{- 4 x y + 1} + 1}{2 x^{2} \left(1 - y\right)^{2}}$$

$$T_{131}(n, m, k) = \begin{cases}1&\text{if n=0, m=0, k=0} ,\ \\0&\text{if k=0} ,\ \\0&\text{if k>0 and m>n} ,\ \\\frac{k {\binom{n}{m}} {\binom{k + n}{m}} {\binom{2 k + 2 m}{2 m}} {\binom{2 k + 2 n}{n}}}{\left(k + n\right) {\binom{k + m}{k}} {\binom{2 k + 2 n}{2 m}}} \end{cases} $$