Generating function
$$U_{546}(x, y) = - \frac{8 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}} \left(x - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}\right)}$$
Explicit formula
$$T_{546}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 2 n\right) {\binom{k + n - 1}{n}} {\binom{- k - 2 m + 2 n - 1}{m - 1}}}{m} \end{cases} $$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | -1 | -2 | -7 | -3 | -143 | -728 |
1 | -3 | -3 | -1 | -42 | -198 | -1001 |
1 | -5 | 0 | -5 | -25 | -126 | -66 |
1 | -7 | 7 | 0 | -7 | -49 | -294 |
1 | -9 | 18 | -3 | 0 | -9 | -84 |
1 | -11 | 33 | -22 | 0 | 0 | -11 |
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