Generating function
$$U_{297}(x, y) = \frac{\sqrt{3} \left(\sqrt{3} \sqrt{y} - \sqrt{- 8 \sqrt{3} x \sqrt{y} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + 3 y}\right)}{6 x \sqrt{y}}$$
Explicit formula
$$T_{297}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{k + 3 m + n - 1}{m}}}{k + 2 m + n}$$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 2 | 7 | 3 | 143 | 728 | 3876 |
2 | 6 | 24 | 11 | 546 | 2856 | 15504 |
5 | 2 | 9 | 44 | 2275 | 1224 | 6783 |
14 | 7 | 35 | 182 | 98 | 54264 | 30723 |
42 | 252 | 1386 | 7644 | 4284 | 244188 | 1413258 |
132 | 924 | 5544 | 3234 | 188496 | 1106028 | 6545616 |
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