Generating function
$$U_{296}(x, y) = \frac{\sqrt{3} \left(\sqrt{3} \sqrt{x} - \sqrt{- 8 \sqrt{3} \sqrt{x} y \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)} + 3 x}\right)}{6 \sqrt{x} y}$$
Explicit formula
$$T_{296}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{k + m + 3 n - 1}{n}}}{k + m + 2 n}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
1 | 2 | 6 | 2 | 7 | 252 | 924 |
3 | 7 | 24 | 9 | 35 | 1386 | 5544 |
12 | 3 | 11 | 44 | 182 | 7644 | 3234 |
55 | 143 | 546 | 2275 | 98 | 4284 | 188496 |
273 | 728 | 2856 | 1224 | 54264 | 244188 | 1106028 |
1428 | 3876 | 15504 | 6783 | 30723 | 1413258 | 6545616 |
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