$$U_{828}(x, y) = \frac{x y - \sqrt{x^{2} y^{2} - 2 x y - 4 x + 1} + 1}{2 x y + 2 x}$$

$$T_{828}(n, m, k) = \frac{k {\binom{n - 1}{m}} {\binom{k - m + 2 n - 1}{- m + n}}}{k + n}$$