Pyramid #363
Generating function
$$U_{363}(x, y) = \frac{y^{2}}{2} + y - \frac{\sqrt{4 x + y^{4} + 4 y^{3} + 6 y^{2} + 4 y + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{363}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{2 k - 4 n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 2 -3 4 -5 6 -7
1 -6 21 -56 126 -252 462
-2 2 -11 44 -143 4004 -1001
5 -7 525 -28 119 -4284 13566
-14 252 -2394 1596 -8379 368676 -1413258
42 -924 10626 -85008 5313 -276276 1243242
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