Pyramid #460
Generating function
$$U_{460}(x, y) = \frac{\left(y + 1\right)^{4} + \sqrt{4 x \left(y + 1\right)^{2} + \left(y + 1\right)^{8}}}{2 \left(y + 1\right)^{2}}$$
Explicit formula
$$T_{460}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\{\binom{2 k}{m}}&\text{if m>0 and n=0} ,\ \\\frac{k {\binom{2 k - 6 n}{m}} {\binom{k - n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
Data table
1 2 1 0 0 0 0
1 -4 1 -2 35 -56 84
-1 1 -55 22 -715 2002 -5005
2 -32 272 -1632 7752 -31008 108528
-5 11 -1265 1012 -6325 3289 -148005
14 -392 5684 -5684 44051 -2819264 15505952
-42 1428 -2499 29988 -277389 21081564 -137030166
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