Pyramid #818
Generating function
$$U_{818}(x, y) = \frac{1}{\sqrt{- \frac{4 x}{\sqrt{1 - 4 y}} + 1}}$$
Explicit formula
$$TA_{984}(n, k) = \begin{cases}{4}^{n} \binom {n+j-1} {n} &\text{if k even, where j =} \frac {k} {2},\\\frac {\binom {n+j} {n} \binom {2n+2j} {n+j}} {\binom {2j} {j}}&\text{if k odd, where j =} \frac {k-1} {2},\end{cases} $$$$T_{818}(n, m, k) = \operatorname{TA_{984}}{\left(m,n \right)} \operatorname{TA_{984}}{\left(n,k \right)}$$
Data table
1 0 0 0 0 0 0
2 4 12 40 140 504 1848
6 24 96 384 1536 6144 24576
20 120 600 2800 12600 55440 240240
70 560 3360 17920 89600 430080 2007040
252 2520 17640 105840 582120 3027024 15135120
924 11088 88704 591360 3548160 19869696 105971712
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