Generating function
$$U_{1362}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x} \left(1 - \sqrt{1 - 4 y}\right)^{3}}{16 y^{3}} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{1362}(n, m, k) = \frac{3 k {\binom{k + 3 n - 1}{n}} {\binom{3 k + 2 m + 6 n - 1}{m}}}{3 k + m + 6 n}$$
Data table
1 3 9 28 9 297 1001
1 9 54 273 126 5508 23256
3 45 405 285 17325 95634 49335
12 252 3024 273 206388 1381212 8457792
55 1485 22275 24552 222156 17494785 124230645
273 9009 162162 2111109 2225223 201675474 1630641012
1428 55692 1169532 17561544 21135114 2167309872 1966633032
Export
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