Pyramid #737
Generating function
$$U_{737}(x, y) = \frac{- 2 x \left(y + 1\right)^{4} - \sqrt{- 4 x \left(y + 1\right)^{4} + 1} + 1}{2 x^{2} \left(y + 1\right)^{6}}$$
Explicit formula
$$T_{737}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{2 k + 4 n}{m}}}{k + n}$$
Data table
1 2 1 0 0 0 0
2 12 3 4 3 12 2
5 5 225 6 105 126 105
14 196 1274 5096 14014 28028 42042
42 756 6426 34272 12852 359856 779688
132 2904 30492 20328 96558 3476088 9848916
429 11154 139425 11154 641355 2821962 9876867
Export
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