Pyramid #723
Generating function
$$U_{723}(x, y) = \frac{1 - \sqrt{y^{2} \left(- 4 x - 4\right) + 1}}{2 y^{2}}$$
Explicit formula
$$T_{723}(n, m, k) = \frac{k \left(\left(-1\right)^{m} + 1\right) {\binom{k + m}{n}} {\binom{k + m - n}{\frac{m}{2}}}}{2 k + 2 m}$$
Data table
1 0 1 0 2 0 5
1 0 2 0 6 0 2
0 0 1 0 6 0 3
0 0 0 0 2 0 2
0 0 0 0 0 0 5
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Export
expand_less