$$U_{82}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{4} - 16 x^{3} - 24 x^{2} - 16 x - 4\right) + 1}}{2 y \left(x + 1\right)^{2}}$$

$$T_{82}(n, m, k) = \frac{k {\binom{2 k + 4 m}{n}} {\binom{k + 2 m - 1}{m}}}{k + m}$$