Pyramid #703
Generating function
$$U_{703}(x, y) = \sqrt{4 x + 1} \left(y + 1\right)$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{703}(n, m, k) = \operatorname{Tsqrt}{\left(n,k \right)} {\binom{k}{m}}$$
Data table
1 1 0 0 0 0 0
2 2 0 0 0 0 0
-2 -2 0 0 0 0 0
4 4 0 0 0 0 0
-10 -10 0 0 0 0 0
28 28 0 0 0 0 0
-84 -84 0 0 0 0 0
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