Generating function
$$U_{1464}(x, y) = \frac{\sqrt{3} \left(2 y + 2\right) \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{1464}(n, m, k) = \frac{k {\binom{2 k + 2 n}{m}} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
1 | 4 | 6 | 4 | 1 | 0 | 0 |
3 | 18 | 45 | 6 | 45 | 18 | 3 |
12 | 96 | 336 | 672 | 84 | 672 | 336 |
55 | 55 | 2475 | 66 | 1155 | 1386 | 1155 |
273 | 3276 | 18018 | 6006 | 135135 | 216216 | 252252 |
1428 | 19992 | 129948 | 519792 | 1429428 | 2858856 | 4288284 |
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