Pyramid #740
Generating function
$$U_{740}(x, y) = \frac{\left(1 - y\right)^{6} \left(- \frac{2 x}{\left(1 - y\right)^{4}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{4}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{740}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + m + 4 n - 1}{m}}}{k + n}$$
Data table
1 2 3 4 5 6 7
2 12 42 112 252 504 924
5 5 275 11 3575 1001 25025
14 196 147 784 3332 119952 379848
42 756 7182 4788 25137 1106028 4239774
132 2904 33396 267168 16698 868296 3907332
429 11154 150579 1405404 10189179 61135074 315864549
Export
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