Generating function
$$U_{892}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 x \left(1 - y\right)}$$
Explicit formula
$$T_{892}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{2 k + m + n - 1}{m}}}{k + n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 6 | 12 | 2 | 3 | 42 | 56 |
7 | 28 | 7 | 14 | 245 | 392 | 588 |
3 | 15 | 45 | 105 | 21 | 378 | 63 |
143 | 858 | 3003 | 8008 | 18018 | 36036 | 66066 |
728 | 5096 | 20384 | 61152 | 15288 | 336336 | 672672 |
3876 | 31008 | 139536 | 46512 | 127908 | 3069792 | 6651216 |
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