Pyramid #928
Generating function
$$U_{928}(x, y) = \sqrt{x^{2} + 4 x y + 2 x + 4 y + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{928}(n, m, k) = \operatorname{Tsqrt}{\left(m,k \right)} {\binom{k - m}{n}}$$
Data table
1 2 -2 4 -10 28 -84
1 0 2 -8 30 -112 420
0 0 -2 12 -60 280 -1260
0 0 2 -16 100 -560 2940
0 0 -2 20 -150 980 -5880
0 0 2 -24 210 -1568 10584
0 0 -2 28 -280 2352 -17640
Export
expand_less