$$U_{537}(x, y) = \frac{y^{2} \left(4 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}}\right)}{\left(1 - \sqrt{1 - 4 y}\right)^{2}}$$

$$T_{537}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 3 n\right) {\binom{k}{n}} {\binom{- k - m + 3 n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$