Generating function
$$U_{899}(x, y) = \frac{\left(1 - y\right) \left(2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2 \operatorname{abs}{\left(y - 1 \right)}} \right)}}{3} \right)}\right)}{3 x}$$
Explicit formula
$$T_{899}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{k + m + 2 n - 1}{m}}}{k + n}$$
1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 6 | 12 | 2 | 3 | 42 | 56 |
7 | 35 | 105 | 245 | 49 | 882 | 147 |
3 | 21 | 84 | 252 | 63 | 1386 | 2772 |
143 | 1287 | 6435 | 23595 | 70785 | 184041 | 429429 |
728 | 8008 | 48048 | 208208 | 728728 | 2186184 | 5829824 |
3876 | 50388 | 352716 | 176358 | 705432 | 23984688 | 71954064 |
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