$$U_{132}(x, y) = \frac{- \sqrt{1 - 4 x} + \sqrt{- 4 x y + 1}}{- 2 x y + 2 x}$$

$$T_{132}(n, m, k) = \begin{cases}0&\text{if n<m} ,\ \\\frac{k {\binom{n}{m}} {\binom{k + n}{m}} {\binom{2 k + 2 m}{2 m}} {\binom{2 k + 2 n}{n}}}{\left(k + n\right) {\binom{k + m}{k}} {\binom{2 k + 2 n}{2 m}}} \end{cases} $$