$$U_{646}(x, y) = \frac{\left(x + 1\right)^{2} \left(\sqrt{4 y + 1} + 1\right)}{2}$$

$$T_{646}(n, m, k) = \begin{cases}\frac{\left(-1\right)^{m - 1} k {\binom{2 k}{n}} {\binom{- k + 2 m - 1}{m - 1}}}{m}&\text{if m>0} ,\ \\{\binom{2 k}{n}}&\text{if m==0} \end{cases} $$