Pyramid #941
Generating function
$$U_{941}(x, y) = 2 x y + \sqrt{4 x^{2} y^{2} + 4 x + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{941}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + m \right)} {\binom{n}{m}}}{k + m}$$
Data table
1 0 0 0 0 0 0
2 2 0 0 0 0 0
-2 0 2 0 0 0 0
4 0 -4 0 0 0 0
-10 0 12 0 -2 0 0
28 0 -40 0 12 0 0
-84 0 140 0 -60 0 4
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