$$U_{421}(x, y) = \frac{\sqrt{- 16 x y + 4 x + 1} + 1}{2 \sqrt{1 - 4 y}}$$

$$T_{421}(n, m, k) = \begin{cases}4^{m} {\binom{\frac{k}{2} + m - 1}{m}}&\text{if n=0} ,\ \\\frac{4^{m} k {\binom{k - n - 1}{n - 1}} {\binom{\frac{k}{2} + m - n - 1}{m}}}{n} \end{cases} $$