Generating function
$$U_{457}(x, y) = \frac{1}{\frac{4 y \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3} - y + 1}$$
Explicit formula
$$T_{457}(n, m, k) = \begin{cases}{\binom{k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} m {\binom{k + m - 1}{m}} {\binom{- m + 3 n - 1}{n - 1}}}{n} \end{cases} $$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 0 | -2 | -3 | -3 | -2 | 0 | 3 |
| 0 | 7 | 1 | 1 | 8 | 5 | 2 |
| 0 | -3 | -42 | -42 | -35 | -25 | -15 |
| 0 | 143 | 198 | 198 | 168 | 126 | 84 |
| 0 | -728 | -1001 | -1001 | -858 | -66 | -462 |
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