Generating function
$$U_{994}(x, y) = \frac{- 2 x \left(y + 1\right) - \sqrt{- 4 x \left(y + 1\right) + 1} + 1}{2 x^{2} \left(y + 1\right)^{4}}$$
Explicit formula
$$T_{994}(n, m, k) = \frac{k {\binom{- 2 k + n}{m}} {\binom{2 k + 2 n}{n}}}{k + n}$$
1 | -2 | 3 | -4 | 5 | -6 | 7 |
2 | -2 | 2 | -2 | 2 | -2 | 2 |
5 | 0 | 0 | 0 | 0 | 0 | 0 |
14 | 14 | 0 | 0 | 0 | 0 | 0 |
42 | 84 | 42 | 0 | 0 | 0 | 0 |
132 | 396 | 396 | 132 | 0 | 0 | 0 |
429 | 1716 | 2574 | 1716 | 429 | 0 | 0 |
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