Pyramid #759
Generating function
$$U_{759}(x, y) = \frac{\left(1 - y\right)^{4} \left(1 - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1}\right)^{3}}{8 x^{3}}$$
Explicit formula
$$T_{759}(n, m, k) = \frac{3 k {\binom{3 k + 2 n}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{3 k + 2 n}$$
Data table
1 2 3 4 5 6 7
3 12 3 6 105 168 252
9 54 189 504 1134 2268 4158
28 224 1008 336 924 22176 48048
9 9 495 198 6435 18018 45045
297 3564 23166 108108 405405 1297296 3675672
1001 14014 105105 56056 238238 8576568 27159132
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