Pyramid #496
Generating function
$$U_{496}(x, y) = - \frac{1}{\left(1 - y\right) \left(\frac{x}{\left(1 - y\right)^{2}} - 1\right)}$$
Explicit formula
$$T_{496}(n, m, k) = \frac{k {\binom{k + n}{n}} {\binom{k + m + 2 n - 1}{m}}}{k + n}$$
Data table
1 1 1 1 1 1 1
1 3 6 1 15 21 28
1 5 15 35 7 126 21
1 7 28 84 21 462 924
1 9 45 165 495 1287 3003
1 11 66 286 1001 3003 8008
1 13 91 455 182 6188 18564
Export
expand_less