$$U_{247}(x, y) = x + y^{2}$$

$$\delta{(a, b)} = \begin{cases}1&\text{if a = b},\\ 0 \end{cases} $$$$T_{247}(n, m, k) = \frac{\left(\left(-1\right)^{m} + 1\right) \delta{\left(k,\frac{m}{2} + n \right)} {\binom{\frac{m}{2} + n}{n}}}{2}$$