$$U_{541}(x, y) = \frac{y^{4} \left(4 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}}\right)}{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}$$

$$T_{541}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m==0 } ,\ \\\frac{2 \left(k - 3 n\right) {\binom{k}{n}} {\binom{2 k + 2 m - 6 n - 1}{m - 1}}}{m} \end{cases} $$