Pyramid #396
Generating function
$$U_{396}(x, y) = \frac{\sqrt{\frac{4 x}{\sqrt{1 - 4 y}} + \frac{1}{1 - 4 y}}}{2} + \frac{1}{2 \sqrt{1 - 4 y}}$$
Explicit formula
$$T_{396}(n, m, k) = \begin{cases}4^{m} {\binom{\frac{k}{2} + m - 1}{m}}&\text{if n=0} ,\ \\\frac{4^{m} k {\binom{k - n - 1}{n - 1}} {\binom{\frac{k}{2} + m - \frac{n}{2} - 1}{m}}}{n} \end{cases} $$
Data table
1 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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