Pyramid #85
Generating function
$$U_{85}(x, y) = \frac{1 - \sqrt{y \left(- 4 x - 2\right) - 2 y \sqrt{4 x + 1} + 1}}{y \left(\sqrt{4 x + 1} + 1\right)}$$
Explicit formula
$$T_{85}(n, m, k) = \begin{cases}1&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k \left(k + 2 m\right) {\binom{k + 2 m - 1}{m}} {\binom{- k - 2 m + 2 n - 1}{n - 1}}}{n \left(k + m\right)} \end{cases} $$
Data table
1 1 1 1 1 1 1
1 3 1 35 126 462 1716
-1 0 1 7 378 1848 858
2 1 0 35 42 3234 20592
-5 -3 0 0 126 231 24024
14 9 2 0 0 462 12012
-42 -28 -1 0 0 0 1716
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