$$U_{422}(x, y) = \frac{1 - \sqrt{- 16 x y + 4 x + 1}}{2 \sqrt{1 - 4 y}}$$

$$T_{422}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{4^{m} k {\binom{k - n - 1}{n - 1}} {\binom{\frac{k}{2} + m - n - 1}{m}}}{n} \end{cases} $$