Generating function
$$U_{1355}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{\left(1 - 4 y\right)^{3}}}}{2} \right)}}{3} \right)}}{3 \sqrt{\frac{x}{\left(1 - 4 y\right)^{3}}} \left(1 - 4 y\right)^{\frac{3}{2}}}$$
Explicit formula
$$T_{1355}(n, m, k) = \frac{4^{m} k {\binom{k + 3 n - 1}{n}} {\binom{\frac{3 k}{2} + m + 3 n - 1}{m}}}{k + 2 n}$$
1 | 4 | 16 | 64 | 256 | 1024 | 4096 |
1 | 16 | 16 | 128 | 896 | 57344 | 344064 |
3 | 84 | 1344 | 16128 | 16128 | 1419264 | 11354112 |
12 | 48 | 1056 | 16896 | 219648 | 24600576 | 24600576 |
55 | 286 | 8008 | 16016 | 256256 | 34850816 | 418209792 |
273 | 17472 | 594048 | 14257152 | 270885888 | 4334174208 | 60678438912 |
1428 | 108528 | 434112 | 12155136 | 267412992 | 49203990528 | 787263848448 |
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