Pyramid #704
Generating function
$$U_{704}(x, y) = - \frac{\sqrt{4 x + 1}}{y \sqrt{4 x + 1} - 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{704}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + m \right)} {\binom{k + m}{m}}}{k + m}$$
Data table
1 1 1 1 1 1 1
2 4 6 8 10 12 14
-2 0 6 16 30 48 70
4 0 -4 0 2 64 140
-10 0 6 0 -10 0 7
28 0 -12 0 12 0 -28
-84 0 28 0 -20 0 28
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