Pyramid #717
Generating function
$$U_{717}(x, y) = - \frac{\sqrt{4 y + 1}}{x \left(4 y + 1\right) - 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{717}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(m,k + 2 n \right)} {\binom{k + n}{n}}}{k + n}$$
Data table
1 2 -2 4 -10 28 -84
1 6 6 -4 6 -12 28
1 10 30 2 -10 12 -20
1 14 70 140 7 -28 28
1 18 126 420 630 252 -84
1 22 198 924 2310 2772 924
1 26 286 1716 6006 12012 12012
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