$$U_{267}(x, y) = \frac{1 - \sqrt{- 4 x^{2} - 4 y + 1}}{2 x^{2} + 2 y}$$

$$T_{267}(n, m, k) = \frac{k \left(\left(-1\right)^{n} + 1\right) {\binom{m + \frac{n}{2}}{m}} {\binom{k + 2 m + n - 1}{m + \frac{n}{2}}}}{2 k + 2 m + n}$$