Generating function
$$U_{891}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 x}$$
Explicit formula
$$T_{891}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{k + m + n - 1}{m}}}{k + n}$$
1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 4 | 6 | 8 | 1 | 12 | 14 |
7 | 21 | 42 | 7 | 105 | 147 | 196 |
3 | 12 | 3 | 6 | 105 | 168 | 252 |
143 | 715 | 2145 | 5005 | 1001 | 18018 | 3003 |
728 | 4368 | 15288 | 40768 | 91728 | 183456 | 336336 |
3876 | 27132 | 108528 | 325584 | 81396 | 1790712 | 3581424 |
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