Generating function
$$U_{192}(x, y) = \frac{2 x y - \sqrt{1 - 4 y} + 1}{2 y}$$
Explicit formula
$$T_{192}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k - 1}{n}} {\binom{- k - m + n - 1}{m - 1}}}{m} \end{cases} $$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
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 | 0 | 0 | 0 | 0 | 0 | 0 |
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