Generating function
$$U_{655}(x, y) = \frac{y \left(3 - 3 \sqrt{- \frac{32 \sqrt{3} x \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}}} + 1}\right)}{8 x \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{655}(n, m, k) = \frac{k \left(k + 3 n\right) {\binom{k + 2 n}{n}} {\binom{k + 3 m + 3 n - 1}{m}}}{\left(k + 2 n\right) \left(k + 2 m + 3 n\right)}$$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 4 | 18 | 88 | 455 | 2448 | 13566 |
2 | 14 | 84 | 49 | 2856 | 16758 | 99176 |
5 | 5 | 375 | 255 | 16625 | 10626 | 67275 |
14 | 182 | 1638 | 1274 | 92092 | 63882 | 4322682 |
42 | 672 | 7056 | 61824 | 4914 | 3683232 | 26581632 |
132 | 2508 | 30096 | 293436 | 254562 | 20525472 | 157582656 |
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