$$U_{469}(x, y) = y \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) + 1$$

$$T_{469}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} m {\binom{k}{m}} {\binom{- m + 3 n - 1}{n - 1}}}{n} \end{cases} $$