Generating function
$$U_{306}(x, y) = - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{y \left(3 x - \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{\sqrt{y}}\right)}$$
Explicit formula
$$T_{306}(n, m, k) = \begin{cases}1&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - n\right) {\binom{k + n - 1}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | -1 | -2 | -7 | -3 | -143 | -728 |
1 | -2 | -3 | -1 | -42 | -198 | -1001 |
1 | -3 | -3 | -1 | -42 | -198 | -1001 |
1 | -4 | -2 | -8 | -35 | -168 | -858 |
1 | -5 | 0 | -5 | -25 | -126 | -66 |
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