Generating function
$$U_{491}(x, y) = \frac{1 - \sqrt{- 4 x \left(y + 1\right)^{3} + 1}}{2 x \left(y + 1\right)^{2}}$$
Explicit formula
$$T_{491}(n, m, k) = \frac{k {\binom{k + 3 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 4 | 6 | 4 | 1 | 0 | 0 |
2 | 14 | 42 | 7 | 7 | 42 | 14 |
5 | 5 | 225 | 6 | 105 | 126 | 105 |
14 | 182 | 1092 | 4004 | 1001 | 18018 | 24024 |
42 | 672 | 504 | 2352 | 7644 | 183456 | 336336 |
132 | 2508 | 22572 | 127908 | 511632 | 1534896 | 3581424 |
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