$$U_{572}(x, y) = \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{8 y^{3}} + \frac{1 - \sqrt{1 - 4 y}}{2 y}$$

$$T_{572}(n, m, k) = \frac{\left(k + 2 n\right) {\binom{k}{n}} {\binom{k + 2 m + 2 n - 1}{m}}}{k + m + 2 n}$$