$$U_{1337}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x} \left(y + 1\right)^{2}}{2} \right)}}{3} \right)}}{3 \sqrt{x}}$$

$$T_{1337}(n, m, k) = \frac{k {\binom{k + 3 n}{n}} {\binom{2 k + 4 n}{m}}}{k + 3 n}$$