$$U_{200}(x, y) = \frac{y + \left(x - 1\right)^{2}}{1 - x}$$

$$T_{200}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0 and k=0 } ,\ \\0&\text{if k=0 } ,\ \\{\binom{k}{m}} {\binom{- k + 2 m + n - 1}{n}} \end{cases} $$