Generating function
$$U_{484}(x, y) = \frac{\frac{2 x}{3} + \frac{\left(y + 1\right)^{4}}{9}}{\sqrt[3]{\frac{x^{2}}{2 \left(y + 1\right)^{2}} + \frac{\sqrt{3} x \sqrt{x \left(27 x + 4 \left(y + 1\right)^{4}\right)}}{18 \left(y + 1\right)^{2}} + \frac{x \left(y + 1\right)^{2}}{3} + \frac{\left(y + 1\right)^{6}}{27}}} + \frac{\left(y + 1\right)^{2}}{3} + \sqrt[3]{\frac{x^{2}}{2 \left(y + 1\right)^{2}} + \frac{\sqrt{3} x \sqrt{x \left(27 x + 4 \left(y + 1\right)^{4}\right)}}{18 \left(y + 1\right)^{2}} + \frac{x \left(y + 1\right)^{2}}{3} + \frac{\left(y + 1\right)^{6}}{27}}$$
Explicit formula
$$T_{484}(n, m, k) = \begin{cases}{\binom{2 k}{m}}&\text{if n=0} ,\ \\\frac{2 k {\binom{2 k - 4 n}{m}} {\binom{2 k - 2 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
2 | -4 | 6 | -8 | 1 | -12 | 14 |
-3 | 18 | -63 | 168 | -378 | 756 | -1386 |
1 | -1 | 55 | -22 | 715 | -2002 | 5005 |
-42 | 588 | -441 | 2352 | -9996 | 359856 | -1139544 |
198 | -3564 | 33858 | -22572 | 118503 | -5214132 | 19987506 |
-1001 | 22022 | -253253 | 2026024 | -1266265 | 6584578 | -29630601 |
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