A213600 Triangle T(n,k) read by rows: Number of Dyck n-paths with midpoint at height k.
1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 4, 0, 9, 0, 1, 0, 25, 0, 16, 0, 1, 25, 0, 81, 0, 25, 0, 1, 0, 196, 0, 196, 0, 36, 0, 1, 196, 0, 784, 0, 400, 0, 49, 0, 1, 0, 1764, 0, 2304, 0, 729, 0, 64, 0, 1, 1764, 0, 8100, 0, 5625, 0, 1225, 0, 81, 0, 1, 0, 17424, 0, 27225, 0, 12100, 0
Offset: 0
Examples
Triangle T(n,k) begins:
1
0 1
1 0 1
0 4 0 1
4 0 9 0 1
0 25 0 16 0 1
25 0 81 0 25 0 1
0 196 0 196 0 36 0 1
196 0 784 0 400 0 49 0 1
0 1764 0 2304 0 729 0 64 0 1
1764 0 8100 0 5625 0 1225 0 81 0 1
...
Crossrefs
Formula
T(n,k) = A053121(n,k)^2.