Pyramid #994
Generating function
$$U_{994}(x, y) = \frac{- 2 x \left(y + 1\right) - \sqrt{- 4 x \left(y + 1\right) + 1} + 1}{2 x^{2} \left(y + 1\right)^{4}}$$
Explicit formula
$$T_{994}(n, m, k) = \frac{k {\binom{- 2 k + n}{m}} {\binom{2 k + 2 n}{n}}}{k + n}$$
Data table
1 -2 3 -4 5 -6 7
2 -2 2 -2 2 -2 2
5 0 0 0 0 0 0
14 14 0 0 0 0 0
42 84 42 0 0 0 0
132 396 396 132 0 0 0
429 1716 2574 1716 429 0 0
Related
Export
expand_less