Generating function
$$U_{1472}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{\left(1 - y\right)^{2}}}}{2} \right)}}{3} \right)}}{3 \sqrt{x} \left(1 - y\right)}$$
Explicit formula
$$T_{1472}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{k + 2 n}$$
Data table
1 2 3 4 5 6 7
1 4 1 2 35 56 84
3 18 63 168 378 756 1386
12 96 432 144 396 9504 20592
55 55 3025 121 39325 11011 275275
273 3276 21294 99372 372645 1192464 3378648
1428 19992 14994 79968 339864 12235104 38744496
Export
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