Generating function
$$U_{995}(x, y) = \frac{\left(x + 1\right)^{2}}{\sqrt{- 4 y \left(x + 1\right) + 1}}$$
Explicit formula
$$TA_{984}(n, k) = \begin{cases}{4}^{n} \binom {n+j-1} {n} &\text{if k even, where j =} \frac {k} {2},\\\frac {\binom {n+j} {n} \binom {2n+2j} {n+j}} {\binom {2j} {j}}&\text{if k odd, where j =} \frac {k-1} {2},\end{cases} $$$$T_{995}(n, m, k) = \operatorname{TA_{984}}{\left(m,k \right)} {\binom{2 k + m}{n}}$$
| 1 | 2 | 6 | 20 | 70 | 252 | 924 |
| 2 | 6 | 24 | 100 | 420 | 1764 | 7392 |
| 1 | 6 | 36 | 200 | 1050 | 5292 | 25872 |
| 0 | 2 | 24 | 200 | 1400 | 8820 | 51744 |
| 0 | 0 | 6 | 100 | 1050 | 8820 | 64680 |
| 0 | 0 | 0 | 20 | 420 | 5292 | 51744 |
| 0 | 0 | 0 | 0 | 70 | 1764 | 25872 |
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