Pyramid #975
Generating function
$$U_{975}(x, y) = \frac{1 - \sqrt{\sqrt{4 y + 1} \left(- 16 x y - 4 x\right) + 1}}{\sqrt{4 y + 1} \left(8 x y + 2 x\right)}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{975}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(m,3 n \right)} {\binom{k + 2 n - 1}{n}}}{k + n}$$
Data table
1 0 0 0 0 0 0
1 6 6 -4 6 -12 28
2 24 96 128 0 0 0
5 90 630 2100 3150 126 -420
14 336 3360 17920 53760 86016 57344
42 1260 16380 120120 540540 1513512 2522520
132 4752 76032 709632 4257792 17031168 45416448
Export
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