$$U_{101}(x, y) = \frac{1}{\sqrt{- 4 x + \left(y - 1\right)^{2}}}$$

$$T_{101}(n, m, k) = 4^{n} {\binom{\frac{k}{2} + n - 1}{n}} {\binom{k + m + 2 n - 1}{m}}$$