Pyramid #370
Generating function
$$U_{370}(x, y) = \frac{\sqrt{4 x y^{4} - 16 x y^{3} + 24 x y^{2} - 16 x y + 4 x + 1} + 1}{2 y^{2} - 4 y + 2}$$
Explicit formula
$$T_{370}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{k - n - 1}{n - 1}} {\binom{2 k + m - 4 n - 1}{m}}}{n} \end{cases} $$
Data table
1 2 3 4 5 6 7
1 -2 1 0 0 0 0
-1 6 -15 2 -15 6 -1
2 -2 9 -24 42 -504 42
-5 7 -455 182 -5005 1001 -15015
14 -252 2142 -11424 4284 -119952 259896
-42 924 -9702 6468 -30723 1106028 -3133746
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