Generating function
$$U_{654}(x, y) = - \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y} \left(\frac{4 x \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y} - 1\right)}$$
Explicit formula
$$T_{654}(n, m, k) = \frac{k \left(k + 2 n\right) {\binom{k + n}{n}} {\binom{k + 3 m + 2 n - 1}{m}}}{\left(k + n\right) \left(k + 2 m + 2 n\right)}$$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 3 | 12 | 55 | 273 | 1428 | 7752 |
1 | 5 | 25 | 13 | 7 | 3876 | 21945 |
1 | 7 | 42 | 245 | 1428 | 8379 | 49588 |
1 | 9 | 63 | 408 | 2565 | 15939 | 9867 |
1 | 11 | 88 | 627 | 4235 | 2783 | 18018 |
1 | 13 | 117 | 91 | 6578 | 4563 | 308763 |
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