Generating function
$$U_{1281}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(y + 1\right)^{3} + 1}\right)^{3}}{8 x^{3} \left(y + 1\right)^{6}}$$
Explicit formula
$$T_{1281}(n, m, k) = \frac{3 k {\binom{3 k + 3 n}{m}} {\binom{3 k + 2 n - 1}{n}}}{3 k + n}$$
Data table
1 3 3 1 0 0 0
3 18 45 6 45 18 3
9 81 324 756 1134 1134 756
28 336 1848 616 1386 22176 25872
9 135 945 4095 12285 27027 45045
297 5346 45441 242352 90882 2544696 5513508
1001 21021 21021 133133 5990985 20369349 54318264
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