$$U_{599}(x, y) = \frac{1 - \sqrt{- 4 x \left(y^{2} + 1\right)^{4} + 1}}{2 x \left(y^{2} + 1\right)^{3}}$$

$$T_{599}(n, m, k) = \frac{k \left(\left(-1\right)^{m} + 1\right) {\binom{k + 4 n}{\frac{m}{2}}} {\binom{k + 2 n - 1}{n}}}{2 k + 2 n}$$