Pyramid #105
Generating function
$$U_{105}(x, y) = \frac{x^{2} - 2 x + y^{2} - 2 y + \left(x + y - 1\right) \sqrt{x^{2} - 2 x + y^{2} + y \left(- 2 x - 2\right) + 1} + 1}{2 x^{2} y^{2}}$$
Explicit formula
$$T_{105}(n, m, k) = \frac{2 k {\binom{2 k + m + n}{m}} {\binom{2 k + m + n}{2 k + m}}}{2 k + m + n}$$
Data table
1 2 3 4 5 6 7
2 8 2 4 7 112 168
3 2 75 21 49 1008 189
4 4 21 784 2352 6048 1386
5 7 49 2352 882 2772 7623
6 112 1008 6048 2772 104544 339768
7 168 189 1386 7623 339768 1288287
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