Generating function
$$U_{1356}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - 4 y}}}{2} \right)}}{3} \right)}}{3 \sqrt{\frac{x}{1 - 4 y}} \sqrt{1 - 4 y}}$$
Explicit formula
$$T_{1356}(n, m, k) = \frac{4^{m} k {\binom{k + 3 n - 1}{n}} {\binom{\frac{k}{2} + m + n - 1}{m}}}{k + 2 n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 4 | 16 | 64 | 256 | 1024 | 4096 |
3 | 24 | 144 | 768 | 384 | 18432 | 86016 |
12 | 144 | 1152 | 768 | 4608 | 258048 | 1376256 |
55 | 88 | 88 | 704 | 4928 | 315392 | 1892352 |
273 | 546 | 6552 | 61152 | 489216 | 35223552 | 23482368 |
1428 | 34272 | 479808 | 5117952 | 46061568 | 368492544 | 2702278656 |
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