Pyramid #326
Generating function
$$U_{326}(x, y) = - \frac{x y}{2} - \frac{x}{2} + \frac{\sqrt{x^{2} y^{2} + x^{2} - 2 x + y \left(- 2 x^{2} - 2 x\right) + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{326}(n, m, k) = \begin{cases}0&\text{if n<m} ,\ \\1&\text{if n=0 and m=0} ,\ \\\left(-1\right)^{n} {\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{- m + n + 1} k {\binom{- k + n - 1}{m - 1}} {\binom{k - m - 1}{- m + n}}}{m} \end{cases} $$
Data table
1 0 0 0 0 0 0
-1 -1 0 0 0 0 0
0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0
0 -1 -3 -1 0 0 0
0 -1 -6 -6 -1 0 0
0 -1 -1 -2 -1 -1 0
Export
expand_less