Pyramid #708
Generating function
$$U_{708}(x, y) = \frac{\sqrt{4 x + 1}}{\left(1 - y\right)^{2}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{708}(n, m, k) = \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 k + m - 1}{m}}$$
Data table
1 2 3 4 5 6 7
2 4 6 8 1 12 14
-2 -4 -6 -8 -10 -12 -14
4 8 12 16 20 24 28
-10 -20 -30 -40 -50 -60 -70
28 56 84 112 140 168 196
-84 -168 -252 -336 -420 -504 -588
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