Pyramid #144
Generating function
$$U_{144}(x, y) = \frac{1 - \sqrt{- 2 y \sqrt{4 x + 1} - 2 y + 1}}{2 y}$$
Explicit formula
$$T_{144}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m - 1}{m}}}{k + m}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{k + 2 m - 1}{m}} {\binom{- k - m + 2 n - 1}{n - 1}}}{n} \end{cases} $$
Data table
1 1 2 5 14 42 132
1 2 6 2 7 252 924
-1 -1 0 1 7 378 1848
2 2 2 0 0 84 924
-5 -5 -6 -5 0 0 0
14 14 18 2 14 0 0
-42 -42 -56 -7 -7 -42 0
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