Pyramid #399
Generating function
$$U_{399}(x, y) = \frac{\sqrt{\frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}}}}{2} + \frac{1 - \sqrt{1 - 4 y}}{4 y}$$
Explicit formula
$$T_{399}(n, m, k) = \begin{cases}1&\text{if m=0 and n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if n>0 } ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k - n}{n}} {\binom{- k - m + n - 1}{m - 1}}}{m} \end{cases} $$
Data table
1 1 2 5 14 42 132
1 1 1 1 1 1 1
-1 -1 -1 -1 -1 -1 -1
2 2 2 2 2 2 2
-5 -5 -5 -5 -5 -5 -5
14 14 14 14 14 14 14
-42 -42 -42 -42 -42 -42 -42
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