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
$$T_{1098}(n, m, k) = \frac{9 k^{2} {\binom{6 k + 2 n}{n}} {\binom{3 k + 2 m - 1}{m}}}{\left(3 k + m\right) \left(3 k + n\right)}$$
Data table
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
Export
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