Pyramid #160
Generating function
$$U_{160}(x, y) = \frac{x^{2} - 2 x + \left(x - 1\right) \sqrt{x^{2} - 2 x - 4 y + 1} + 1}{2 y}$$
Explicit formula
$$T_{160}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{2 m + n - 1}{n}}}{k + m}$$
Data table
1 1 2 5 14 42 132
0 2 8 3 112 42 1584
0 3 2 105 504 231 10296
0 4 4 28 168 924 48048
0 5 7 63 462 3003 18018
0 6 112 126 11088 84084 576576
0 7 168 231 24024 21021 1633632
Export
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