$$U_{641}(x, y) = \frac{\sqrt{4 y + 1} + 1}{2 \sqrt{1 - 4 x}}$$

$$T_{641}(n, m, k) = \begin{cases}4^{n} {\binom{\frac{k}{2} + n - 1}{n}}&\text{if m==0 } ,\ \\\frac{\left(-1\right)^{m - 1} \cdot 4^{n} k {\binom{- k + 2 m - 1}{m - 1}} {\binom{\frac{k}{2} + n - 1}{n}}}{m}&\text{if m>0} \end{cases} $$