Pyramid #179
Generating function
$$U_{179}(x, y) = \frac{x y - 2 x - \sqrt{x^{2} y^{2} - 2 x y + 4 x + 1} - 1}{2 y - 2}$$
Explicit formula
$$T_{179}(n, m, k) = \begin{cases}1&\text{if n=0,m=0} ,\ \\\frac{\left(-1\right)^{n} \left(-1\right)^{m - 1} k {\binom{- 2 k - m + 2 n}{n}} {\binom{- k + n - 1}{m - 1}}}{m}&\text{if m>0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k - 2 m + 2 n - 1}{n - 1}}}{n}&\text{if m=0} \end{cases} $$
Data table
1 1 1 1 1 1 1
2 1 1 1 1 1 1
-1 0 0 0 0 0 0
2 -1 0 0 0 0 0
-5 5 -1 0 0 0 0
14 -21 9 -1 0 0 0
-42 84 -56 14 -1 0 0
Export
expand_less