Pyramid #436
Generating function
$$U_{436}(x, y) = \frac{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + \left(x - 1\right) \sqrt{x^{6} - 6 x^{5} + 15 x^{4} - 20 x^{3} + 15 x^{2} - 6 x - 4 y + 1} + 1}{2 y}$$
Explicit formula
$$T_{436}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{2 k + 6 m + n - 1}{n}}}{k + 2 m}$$
Data table
1 1 2 5 14 42 132
2 8 28 1 364 1344 5016
3 36 21 105 4914 22176 97812
4 12 112 77 45864 251328 130416
5 33 476 44275 332514 219912 1336764
6 792 17136 21252 1995084 15833664 112288176
7 1716 54264 8855 10307934 97640928 804731928
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