Pyramid #442
Generating function
$$U_{442}(x, y) = \frac{x^{2} - 2 x - 2 y + \left(x - 1\right) \sqrt{x^{2} - 2 x - 4 y + 1} + 1}{2 y^{2}}$$
Explicit formula
$$T_{442}(n, m, k) = \frac{k {\binom{2 k + 2 m}{m}} {\binom{2 k + 2 m + n - 1}{n}}}{k + m}$$
Data table
1 2 5 14 42 132 429
2 8 3 112 42 1584 6006
3 2 105 504 231 10296 45045
4 4 28 168 924 48048 24024
5 7 63 462 3003 18018 102102
6 112 126 11088 84084 576576 3675672
7 168 231 24024 21021 1633632 11639628
Export
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