$$U_{57}(x, y) = \frac{x + \sqrt{x^{2} - 2 x - 4 y + 1} - 1}{y \left(2 x - 2\right)}$$

$$T_{57}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{2 k + 2 m + n - 1}{n}}}{k + 2 m}$$