Pyramid #998
Generating function
$$U_{998}(x, y) = \frac{1 - y}{- \frac{x}{1 - y} + 1}$$
Explicit formula
$$T_{998}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{- k + m + n - 1}{m}}$$
Data table
1 -1 0 0 0 0 0
1 0 0 0 0 0 0
1 1 1 1 1 1 1
1 2 3 4 5 6 7
1 3 6 1 15 21 28
1 4 1 2 35 56 84
1 5 15 35 7 126 21
Export
expand_less