Pyramid #397
Generating function
$$U_{397}(x, y) = - \frac{\sqrt{\frac{4 x}{\sqrt{1 - 4 y}} + \frac{1}{1 - 4 y}}}{2} + \frac{1}{2 \sqrt{1 - 4 y}}$$
Explicit formula
$$T_{397}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{4^{m} k {\binom{k - n - 1}{n - 1}} {\binom{\frac{k}{2} + m - \frac{n}{2} - 1}{m}}}{n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 0 0 0 0 0 0
1 0 0 0 0 0 0
-2 8 0 0 0 0 0
5 -2 0 0 0 0 0
-14 112 -224 0 0 0 0
42 -336 672 0 0 0 0
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