Pyramid #956
Generating function
$$U_{956}(x, y) = \frac{1 - \sqrt{1 - 4 \left(x + y\right)^{2}}}{2 \left(x + y\right)^{2}}$$
Explicit formula
$$T_{956}(n, m, k) = \begin{cases}\frac{2 k {\binom{m + n}{m}} {\binom{k + m + n - 1}{\frac{m}{2} + \frac{n}{2}}}}{2 k + m + n}&\text{if n + m even} ,\ \\0 \end{cases} $$
Data table
1 0 1 0 2 0 5
0 2 0 8 0 30 0
1 0 12 0 75 0 392
0 8 0 100 0 784 0
2 0 75 0 980 0 8820
0 30 0 784 0 10584 0
5 0 392 0 8820 0 121968
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