Generating function
$$U_{1472}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{\left(1 - y\right)^{2}}}}{2} \right)}}{3} \right)}}{3 \sqrt{x} \left(1 - y\right)}$$
Explicit formula
$$T_{1472}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{k + 2 n}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
1 | 4 | 1 | 2 | 35 | 56 | 84 |
3 | 18 | 63 | 168 | 378 | 756 | 1386 |
12 | 96 | 432 | 144 | 396 | 9504 | 20592 |
55 | 55 | 3025 | 121 | 39325 | 11011 | 275275 |
273 | 3276 | 21294 | 99372 | 372645 | 1192464 | 3378648 |
1428 | 19992 | 14994 | 79968 | 339864 | 12235104 | 38744496 |
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