Pyramid #960
Generating function
$$U_{960}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{3} - 4 x\right) + 1}}{2 x y}$$
Explicit formula
$$T_{960}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m}{\frac{m}{2} + \frac{n}{2}}} {\binom{\frac{m}{2} + \frac{n}{2}}{m}}}{k + 2 m}&\text{if n + m even} ,\ \\0 \end{cases} $$
Data table
1 0 0 0 0 0 0
0 1 0 0 0 0 0
1 0 2 0 0 0 0
0 2 0 5 0 0 0
0 0 6 0 14 0 0
0 1 0 20 0 42 0
0 0 6 0 70 0 132
Export
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