Pyramid #26
Generating function
$$U_{26}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{3} - 8 x^{2} - 4 x\right) + 1}}{x y \left(2 x + 2\right)}$$
Explicit formula
$$T_{26}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 2 m}{- m + n}}}{k + 2 m}$$
Data table
1 0 0 0 0 0 0
1 1 0 0 0 0 0
0 3 2 0 0 0 0
0 3 1 5 0 0 0
0 1 2 35 14 0 0
0 0 2 105 126 42 0
0 0 1 175 504 462 132
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