Pyramid #607
Generating function
$$U_{607}(x, y) = \frac{- \sqrt{- \frac{4 x}{\left(1 - 4 y\right)^{\frac{3}{2}}} + \frac{1}{\left(1 - 4 y\right)^{2}}} + \frac{1}{1 - 4 y}}{2 x}$$
Explicit formula
$$T_{607}(n, m, k) = \frac{4^{m} k {\binom{k + 2 n - 1}{n}} {\binom{\frac{k}{2} + m - \frac{n}{2} - 1}{m}}}{k + n}$$
Data table
1 0 0 0 0 0 0
1 0 0 0 0 0 0
2 0 0 0 0 0 0
5 -2 0 0 0 0 0
14 -56 0 0 0 0 0
42 -336 672 0 0 0 0
132 -1056 2112 0 0 0 0
Export
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