Generating function
$$U_{731}(x, y) = \frac{- 2 x y^{2} - 4 x y - 2 x - \sqrt{- 4 x y^{2} - 8 x y - 4 x + 1} + 1}{2 x^{2} y^{3} + 6 x^{2} y^{2} + 6 x^{2} y + 2 x^{2}}$$
Explicit formula
$$T_{731}(n, m, k) = \frac{k {\binom{k + 2 n}{m}} {\binom{2 k + 2 n}{n}}}{k + n}$$
1 | 1 | 0 | 0 | 0 | 0 | 0 |
2 | 6 | 6 | 2 | 0 | 0 | 0 |
5 | 25 | 5 | 5 | 25 | 5 | 0 |
14 | 98 | 294 | 49 | 49 | 294 | 98 |
42 | 378 | 1512 | 3528 | 5292 | 5292 | 3528 |
132 | 1452 | 726 | 2178 | 4356 | 60984 | 60984 |
429 | 5577 | 33462 | 122694 | 306735 | 552123 | 736164 |
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