$$U_{61}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{2} - 8 x - 4\right) + 1}}{2 y}$$

$$T_{61}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\0&\text{if k=0} ,\ \\\frac{k {\binom{k + 2 m}{m}} {\binom{2 k + 2 m}{n}}}{k + 2 m} \end{cases} $$