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
$$T_{1356}(n, m, k) = \frac{4^{m} k {\binom{k + 3 n - 1}{n}} {\binom{\frac{k}{2} + m + n - 1}{m}}}{k + 2 n}$$
Data table
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
Export
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