Pyramid #751
Generating function
$$U_{751}(x, y) = \frac{\left(\frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{2 y^{2}} + 1\right)^{2} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{2 y^{2}}$$
Explicit formula
$$T_{751}(n, m, k) = \frac{\left(k + n\right) {\binom{2 k}{n}} {\binom{2 k + 2 m + 2 n}{m}}}{k + m + n}$$
Data table
1 2 5 14 42 132 429
2 8 28 96 33 1144 4004
1 6 27 11 429 1638 6188
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Export
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