$$U_{540}(x, y) = - \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{y^{6} \left(8 x - \frac{2 \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}}\right)}$$

$$T_{540}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}}&\text{if m==0} ,\ \\\frac{2 \left(k - 2 n\right) {\binom{k + n - 1}{n}} {\binom{2 k + 2 m - 4 n - 1}{m - 1}}}{m} \end{cases} $$