Pyramid #995
Generating function
$$U_{995}(x, y) = \frac{\left(x + 1\right)^{2}}{\sqrt{- 4 y \left(x + 1\right) + 1}}$$
Explicit formula
$$TA_{984}(n, k) = \begin{cases}{4}^{n} \binom {n+j-1} {n} &\text{if k even, where j =} \frac {k} {2},\\\frac {\binom {n+j} {n} \binom {2n+2j} {n+j}} {\binom {2j} {j}}&\text{if k odd, where j =} \frac {k-1} {2},\end{cases} $$$$T_{995}(n, m, k) = \operatorname{TA_{984}}{\left(m,k \right)} {\binom{2 k + m}{n}}$$
Data table
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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