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
$$T_{1355}(n, m, k) = \frac{4^{m} k {\binom{k + 3 n - 1}{n}} {\binom{\frac{3 k}{2} + m + 3 n - 1}{m}}}{k + 2 n}$$
Data table
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
Export
expand_less