Pyramid #761
Generating function
$$U_{761}(x, y) = \frac{y^{4} \left(1 - \sqrt{- \frac{2 x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{y^{2}} + 1}\right)^{3}}{2 x^{3} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}$$
Explicit formula
$$T_{761}(n, m, k) = \frac{3 k \left(k + n\right) {\binom{3 k + 2 n}{n}} {\binom{2 k + 2 m + 2 n}{m}}}{\left(3 k + 2 n\right) \left(k + m + n\right)}$$
Data table
1 2 5 14 42 132 429
3 12 42 144 495 1716 6006
9 54 243 99 3861 14742 55692
28 224 1232 5824 2548 106624 434112
9 9 585 315 153 69768 305235
297 3564 2673 161568 863379 4266108 19987506
1001 14014 119119 798798 4659655 24818794 12409397
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