Pyramid #19
Pyramid #20
Pyramid #21
Generating function
$$U_{20}(x, y) = \frac{1 - \sqrt{- 4 x - 4 y + 1}}{2 x + 2 y}$$
Explicit formula
$$T_{20}(n, m, k) = \frac{k {\binom{m + n}{m}} {\binom{k + 2 m + 2 n - 1}{m + n}}}{k + m + n}$$
Data table
1 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
Related
Pyramid #21: Left on x
Pyramid #22: Left on y
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