$$U_{213}(x, y) = \frac{1}{\sqrt{- y \left(4 x + 4\right) + 1}}$$

$$T_{213}(n, m, k) = \begin{cases}\frac{{\binom{m}{n}} {\binom{\frac{k}{2} + m}{m}} {\binom{k + 2 m}{\frac{k}{2} + m}}}{{\binom{k}{\frac{k}{2}}}}&\text{if k even} ,\ \\\frac{{\binom{m}{n}} {\binom{\frac{k}{2} + m - \frac{1}{2}}{m}} {\binom{k + 2 m - 1}{\frac{k}{2} + m - \frac{1}{2}}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$