Pyramid #611
Generating function
$$U_{611}(x, y) = \frac{\sqrt{1 - 4 y} \left(- \sqrt{4 x + \frac{1}{\left(1 - 4 y\right)^{2}}} + \frac{1}{1 - 4 y}\right)}{2}$$
Explicit formula
$$T_{611}(n, m, k) = \begin{cases}0&\text{if n < k} ,\ \\- \frac{4^{m} k {\binom{k - n - 1}{n - 1}} {\binom{\frac{k}{2} + m - 2 n - 1}{m}}}{n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 4 0 0 0 0 0
1 -12 48 -64 0 0 0
-2 4 -32 128 -256 2048 0
5 -14 168 -112 448 -10752 14336
-14 504 -8064 75264 -451584 1806336 -4816896
42 -1848 3696 -44352 354816 -19869696 79478784
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