Pyramid #954
Generating function
$$U_{954}(x, y) = \frac{1}{1 - \left(x + y\right)^{2}}$$
Explicit formula
$$T_{954}(n, m, k) = \begin{cases}{\binom{m + n}{m}} {\binom{k + \frac{m}{2} + \frac{n}{2} - 1}{\frac{m}{2} + \frac{n}{2}}}&\text{if n + m even} ,\ \\0 \end{cases} $$
Data table
1 0 1 0 1 0 1
0 2 0 4 0 6 0
1 0 6 0 15 0 28
0 4 0 2 0 56 0
1 0 15 0 7 0 21
0 6 0 56 0 252 0
1 0 28 0 21 0 924
Export
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