$$U_{274}(x, y) = x^{2} + x + y^{3}$$

$$\delta{(a, b)} = \begin{cases}1&\text{if a = b},\\ 0 \end{cases} $$$$T_{274}(n, m, k) = \delta{\left(0,{\binom{m}{3}} \right)} {\binom{k}{\frac{m}{3}}} {\binom{k - \frac{m}{3}}{- k + \frac{m}{3} + n}}$$