Pyramid #93
Generating function
$$U_{93}(x, y) = \frac{- 2 x - 2 y - \sqrt{- 4 x - 4 y + 1} + 1}{2 x + 2 y}$$
Explicit formula
$$T_{93}(n, m, k) = \begin{cases}0&\text{if n=0,m=0} ,\ \\\frac{k {\binom{m + n}{m}} {\binom{2 m + 2 n}{- k + m + n}}}{m + n} \end{cases} $$
Data table
0 1 2 5 14 42 132
1 4 15 56 21 792 3003
2 15 84 42 198 9009 4004
5 56 42 264 15015 8008 408408
14 21 198 15015 1001 612612 352716
42 792 9009 8008 612612 4232592 27159132
132 3003 4004 408408 352716 27159132 192203088
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