Pyramid #927
Generating function
$$U_{927}(x, y) = \frac{i x + i}{\sqrt{4 x y + 4 y - 1}}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{927}(n, m, k) = \frac{k \operatorname{Tsqrt_{2}}{\left(m,k + m \right)} {\binom{k + m}{n}}}{k + m}$$
Data table
1 2 6 20 70 252 924
1 4 18 80 350 1512 6468
0 2 18 120 700 3780 19404
0 0 6 80 700 5040 32340
0 0 0 20 350 3780 32340
0 0 0 0 70 1512 19404
0 0 0 0 0 252 6468
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