Generating function
$$U_{734}(x, y) = \frac{- 2 x - y^{3} + 3 y^{2} - y \left(3 - 2 x\right) + \left(- y^{2} + 2 y - 1\right) \sqrt{- 4 x + y^{2} - 2 y + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{734}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{k + m + 2 n - 1}{m}}}{k + n}$$
1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 6 | 12 | 2 | 3 | 42 | 56 |
5 | 25 | 75 | 175 | 35 | 63 | 105 |
14 | 98 | 392 | 1176 | 294 | 6468 | 12936 |
42 | 378 | 189 | 693 | 2079 | 54054 | 126126 |
132 | 1452 | 8712 | 37752 | 132132 | 396396 | 1057056 |
429 | 5577 | 39039 | 195195 | 78078 | 2654652 | 7963956 |
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