Pyramid #734
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
$$T_{734}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{k + m + 2 n - 1}{m}}}{k + n}$$
Data table
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
Export
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