$$U_{13}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{2} - 8 x - 4\right) + 1}}{y \left(2 x + 2\right)}$$

$$T_{13}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 2 m}{n}}}{k + 2 m}$$