Generating function
$$U_{788}(x, y) = \left(y + 1\right)^{2} \left(\frac{x}{\left(y + 1\right)^{2}} + 1\right)^{3}$$
Explicit formula
$$T_{788}(n, m, k) = \begin{cases}{\binom{2 k - 2 n}{m}}&\text{if n=0} ,\ \\\frac{3 \left(-1\right)^{n - 1} k {\binom{2 k - 2 n}{m}} {\binom{- 3 k + n - 1}{n - 1}}}{n} \end{cases} $$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
3 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | -6 | 9 | -12 | 15 | -18 | 21 |
1 | -4 | 1 | -2 | 35 | -56 | 84 |
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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