Pyramid #372
Generating function
$$U_{372}(x, y) = \frac{\sqrt{4 x^{4} y - 16 x^{3} y + 24 x^{2} y - 16 x y + 4 y + 1} + 1}{2 x^{2} - 4 x + 2}$$
Explicit formula
$$T_{372}(n, m, k) = \begin{cases}{\binom{2 k + n - 1}{n}}&\text{if m=0} ,\ \\\frac{k {\binom{k - m - 1}{m - 1}} {\binom{2 k - 4 m + n - 1}{n}}}{m},\ \\1&\text{if n=0,m=0} \end{cases} $$
Data table
1 1 -1 2 -5 14 -42
2 -2 6 -2 7 -252 924
3 1 -15 9 -455 2142 -9702
4 0 2 -24 182 -11424 6468
5 0 -15 42 -5005 4284 -30723
6 0 6 -504 1001 -119952 1106028
7 0 -1 42 -15015 259896 -3133746
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