$$U_{573}(x, y) = \frac{\sqrt{1 - 4 y} - 1}{y \left(\frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{4 y^{3}} - 2\right)}$$

$$T_{573}(n, m, k) = \frac{\left(k + 3 n\right) {\binom{k + n - 1}{n}} {\binom{k + 2 m + 3 n - 1}{m}}}{k + m + 3 n}$$