$$U_{919}(x, y) = \frac{1 - \sqrt{y \left(- 8 x - 8\right) + 1}}{4 y}$$

$$T_{919}(n, m, k) = \frac{2^{m} k {\binom{k + m}{n}} {\binom{k + 2 m - 1}{m}}}{k + m}$$