Pyramid #731
Generating function
$$U_{731}(x, y) = \frac{- 2 x y^{2} - 4 x y - 2 x - \sqrt{- 4 x y^{2} - 8 x y - 4 x + 1} + 1}{2 x^{2} y^{3} + 6 x^{2} y^{2} + 6 x^{2} y + 2 x^{2}}$$
Explicit formula
$$T_{731}(n, m, k) = \frac{k {\binom{k + 2 n}{m}} {\binom{2 k + 2 n}{n}}}{k + n}$$
Data table
1 1 0 0 0 0 0
2 6 6 2 0 0 0
5 25 5 5 25 5 0
14 98 294 49 49 294 98
42 378 1512 3528 5292 5292 3528
132 1452 726 2178 4356 60984 60984
429 5577 33462 122694 306735 552123 736164
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