$$U_{582}(x, y) = \frac{x}{\left(1 - 4 y\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{1 - 4 y}}$$

$$T_{582}(n, m, k) = 4^{m} {\binom{k}{n}} {\binom{\frac{k}{2} + m + n - 1}{m}}$$