Pyramid #846
Generating function
$$U_{846}(x, y) = \frac{1 - \sqrt{- \frac{4 x}{1 - y} + 1}}{2 x \left(1 - y\right)^{2}}$$
Explicit formula
$$T_{846}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{3 k + m + n - 1}{m}}}{k + n}$$
Data table
1 3 6 1 15 21 28
1 4 1 2 35 56 84
2 1 3 7 14 252 42
5 3 105 28 63 126 231
14 98 392 1176 294 6468 12936
42 336 1512 504 1386 33264 72072
132 1188 594 2178 6534 169884 396396
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