Pyramid #718
Generating function
$$U_{718}(x, y) = \frac{1 - \sqrt{- 4 x \left(4 y + 1\right)^{\frac{3}{2}} + 1}}{2 x \left(4 y + 1\right)}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{718}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(m,k + 3 n \right)} {\binom{k + 2 n}{n}}}{k + 2 n}$$
Data table
1 2 -2 4 -10 28 -84
1 8 16 0 0 0 0
2 28 140 280 14 -56 56
5 100 800 3200 6400 512 0
14 364 4004 24024 84084 168168 168168
42 1344 18816 150528 752640 2408448 4816896
132 5016 85272 852720 5542680 24387792 73163376
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