Generating function
$$U_{1333}(x, y) = \frac{x}{1 - y} + \frac{1}{\left(1 - y\right)^{5}}$$
Explicit formula
$$T_{1333}(n, m, k) = {\binom{k}{n}} {\binom{5 k + m - 4 n - 1}{m}}$$
Data table
1 5 15 35 7 126 21
1 1 1 1 1 1 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 0 0 0
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