Pyramid #936
Generating function
$$U_{936}(x, y) = \sqrt{4 x + 4 y + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{936}(n, m, k) = \operatorname{Tsqrt}{\left(m + n,k \right)} {\binom{m + n}{m}}$$
Data table
1 2 -2 4 -10 28 -84
2 -4 12 -40 140 -504 1848
-2 12 -60 280 -1260 5544 -24024
4 -40 280 -1680 9240 -48048 240240
-10 140 -1260 9240 -60060 360360 -2042040
28 -504 5544 -48048 360360 -2450448 15519504
-84 1848 -24024 240240 -2042040 15519504 -108636528
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