Pyramid #466
Generating function
$$U_{466}(x, y) = \frac{1 - \sqrt{- 4 x y^{4} - 16 x y^{3} - 24 x y^{2} - 16 x y - 4 x + 1}}{2 x y + 2 x}$$
Explicit formula
$$T_{466}(n, m, k) = \frac{k {\binom{3 k + 4 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
Data table
1 3 3 1 0 0 0
1 7 21 35 35 21 7
2 22 110 330 660 924 924
5 75 525 2275 6825 15015 25025
14 266 2394 13566 54264 162792 379848
42 966 10626 74382 371910 1413258 4239774
132 3564 46332 386100 2316600 10656360 39073320
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