Generating function
$$U_{1464}(x, y) = \frac{\sqrt{3} \left(2 y + 2\right) \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{1464}(n, m, k) = \frac{k {\binom{2 k + 2 n}{m}} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
Data table
1 2 1 0 0 0 0
1 4 6 4 1 0 0
3 18 45 6 45 18 3
12 96 336 672 84 672 336
55 55 2475 66 1155 1386 1155
273 3276 18018 6006 135135 216216 252252
1428 19992 129948 519792 1429428 2858856 4288284
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