Generating function
$$U_{1098}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3} \left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{3}}{64 x^{6} y^{3}}$$
Explicit formula
$$T_{1098}(n, m, k) = \frac{9 k^{2} {\binom{6 k + 2 n}{n}} {\binom{3 k + 2 m - 1}{m}}}{\left(3 k + m\right) \left(3 k + n\right)}$$
1 | 3 | 9 | 28 | 9 | 297 | 1001 |
6 | 18 | 54 | 168 | 54 | 1782 | 6006 |
27 | 81 | 243 | 756 | 243 | 8019 | 27027 |
11 | 33 | 99 | 308 | 99 | 3267 | 11011 |
429 | 1287 | 3861 | 12012 | 3861 | 127413 | 429429 |
1638 | 4914 | 14742 | 45864 | 14742 | 486486 | 1639638 |
6188 | 18564 | 55692 | 173264 | 55692 | 1837836 | 6194188 |
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