Pyramid #974
Generating function
$$U_{974}(x, y) = \frac{1}{\left(- x \left(4 y + 1\right)^{\frac{3}{2}} + 1\right)^{2}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{974}(n, m, k) = \operatorname{Tsqrt}{\left(m,3 n \right)} {\binom{2 k + n - 1}{n}}$$
Data table
1 0 0 0 0 0 0
2 12 12 -8 12 -24 56
3 36 144 192 0 0 0
4 72 504 1680 2520 1008 -336
5 120 1200 6400 19200 30720 2048
6 180 2340 17160 77220 216216 360360
7 252 4032 37632 225792 903168 2408448
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