Generating function
$$U_{1264}(x, y) = \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4} \left(- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}} + 1\right)^{3}}$$
Explicit formula
$$T_{1264}(n, m, k) = \frac{\left(2 k + 2 n\right) {\binom{3 k + n - 1}{n}} {\binom{4 k + 2 m + 4 n}{m}}}{2 k + m + 2 n}$$
1 | 4 | 14 | 48 | 165 | 572 | 2002 |
3 | 24 | 132 | 624 | 273 | 11424 | 46512 |
6 | 72 | 54 | 3264 | 17442 | 86184 | 403788 |
1 | 16 | 152 | 112 | 7084 | 4048 | 21528 |
15 | 3 | 345 | 3 | 219375 | 142506 | 849555 |
21 | 504 | 6804 | 68208 | 56637 | 4124736 | 27269088 |
28 | 784 | 12152 | 137984 | 128282 | 10355856 | 75232248 |
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