Generating function
$$U_{1396}(x, y) = \frac{\frac{y}{\left(1 - x\right)^{3}} + 1}{\left(1 - x\right)^{3}}$$
Explicit formula
$$T_{1396}(n, m, k) = {\binom{k}{m}} {\binom{3 k + 3 m + n - 1}{n}}$$
Data table
1 1 0 0 0 0 0
3 6 0 0 0 0 0
6 21 0 0 0 0 0
1 56 0 0 0 0 0
15 126 0 0 0 0 0
21 252 0 0 0 0 0
28 462 0 0 0 0 0
Export
expand_less