Generating function
$$U_{748}(x, y) = \frac{x^{2} \left(1 - \sqrt{1 - 4 y}\right)^{3}}{8 y^{3}} + \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{2 y^{2}} + \frac{1 - \sqrt{1 - 4 y}}{2 y}$$
Explicit formula
$$T_{748}(n, m, k) = \frac{\left(k + n\right) {\binom{2 k}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
2 | 4 | 1 | 28 | 84 | 264 | 858 |
1 | 3 | 9 | 28 | 9 | 297 | 1001 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
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