Pyramid #164
Generating function
$$U_{164}(x, y) = \frac{- x^{3} + 3 x^{2} - 3 x + \left(x - 1\right) \sqrt{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + y \left(4 x - 4\right) + 1} + 1}{2 y}$$
Explicit formula
$$T_{164}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{3 m + n - 1}{n}}}{k + m}$$
Data table
1 1 2 5 14 42 132
0 3 12 45 168 63 2376
0 6 42 225 1092 504 22572
0 1 112 825 5096 2856 15048
0 15 252 2475 1911 12852 79002
0 21 504 6435 61152 488376 3476088
0 28 924 15015 173264 162792 13325004
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