Generating function
$$U_{1007}(x, y) = \left(x + 1\right)^{2} \left(y + 1\right)^{2}$$
Explicit formula
$$T_{1007}(n, m, k) = {\binom{2 k}{m}} {\binom{2 k}{n}}$$
Data table
1 2 1 0 0 0 0
2 4 2 0 0 0 0
1 2 1 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Export
expand_less