Pyramid #139
Generating function
$$U_{139}(x, y) = \frac{- 2 x - y - \sqrt{- 4 x + y^{2} - y \left(2 - 4 x\right) + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{139}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m - 1}{m}}}{k + m}&\text{if n=0} ,\ \\\frac{k {\binom{2 k + 2 n}{n}} {\binom{k + m + n}{m}}}{k + m + n} \end{cases} $$
Data table
1 1 2 5 14 42 132
2 4 6 8 1 12 14
5 15 3 5 75 105 14
14 56 14 28 49 784 1176
42 21 63 147 294 5292 882
132 792 2772 7392 16632 33264 60984
429 3003 12012 36036 9009 198198 396396
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