Pyramid #760
Generating function
$$U_{760}(x, y) = \frac{y^{2} \left(1 - \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1}\right)^{3}}{2 x^{3} \left(1 - \sqrt{1 - 4 y}\right)^{2}}$$
Explicit formula
$$T_{760}(n, m, k) = \frac{3 k \left(k + n\right) {\binom{3 k + 2 n}{n}} {\binom{k + 2 m + n - 1}{m}}}{\left(3 k + 2 n\right) \left(k + m + n\right)}$$
Data table
1 1 2 5 14 42 132
3 6 15 42 126 396 1287
9 27 81 252 81 2673 9009
28 112 392 1344 462 16016 56056
9 45 18 675 2475 9009 3276
297 1782 8019 3267 127413 486486 1837836
1001 7007 35035 154154 637637 2550548 10005996
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