$$U_{121}(x, y) = \frac{1 - \sqrt{- 4 y \sqrt{4 x + 1} + 1}}{2 y}$$

$$T_{121}(n, m, k) = \frac{4^{n} k {\binom{\frac{k}{2} + \frac{m}{2}}{n}} {\binom{k + 2 m - 1}{m}}}{k + m}$$