$$U_{1367}(x, y) = \frac{\left(y + 1\right)^{2}}{\sqrt{1 - 4 x}}$$

$$T_{1367}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 , k=0} ,\ \\4^{n} {\binom{2 k}{m}} {\binom{\frac{k}{2} + n - 1}{n}}&\text{if k even} ,\ \\\frac{{\binom{2 k}{m}} {\binom{\frac{k}{2} + n - \frac{1}{2}}{n}} {\binom{k + 2 n - 1}{\frac{k}{2} + n - \frac{1}{2}}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$