Pyramid #835
Generating function
$$U_{835}(x, y) = \frac{- y^{3} + 3 y^{2} - 3 y - \sqrt{- 4 x + y^{6} - 6 y^{5} + 15 y^{4} - 20 y^{3} + 15 y^{2} + y \left(4 x - 6\right) + 1} + 1}{2 x y^{2} - 4 x y + 2 x}$$
Explicit formula
$$T_{835}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{4 k + m + 5 n - 1}{m}}}{k + n}$$
Data table
1 4 1 2 35 56 84
1 9 45 165 495 1287 3003
2 28 21 112 476 17136 54264
5 95 95 665 36575 168245 67298
14 336 42 364 2457 137592 665028
42 1218 1827 18879 151032 9968112 56485968
132 4488 7854 94248 871794 66256344 430666236
Export
expand_less