$$U_{619}(x, y) = \frac{1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}}{\left(1 - x\right)^{2}}$$

$$T_{619}(n, m, k) = \begin{cases}{\binom{2 k + n - 1}{n}}&\text{if m=0 } ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 3 m - 1}{m - 1}} {\binom{2 k + n - 1}{n}}}{m}&\text{if m>0} \end{cases} $$