This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A213600 #13 Oct 07 2022 15:48:45 %S A213600 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, %T A213600 196,0,36,0,1,196,0,784,0,400,0,49,0,1,0,1764,0,2304,0,729,0,64,0,1, %U A213600 1764,0,8100,0,5625,0,1225,0,81,0,1,0,17424,0,27225,0,12100,0 %N A213600 Triangle T(n,k) read by rows: Number of Dyck n-paths with midpoint at height k. %F A213600 T(n,k) = A053121(n,k)^2. %e A213600 Triangle T(n,k) begins: %e A213600 1 %e A213600 0 1 %e A213600 1 0 1 %e A213600 0 4 0 1 %e A213600 4 0 9 0 1 %e A213600 0 25 0 16 0 1 %e A213600 25 0 81 0 25 0 1 %e A213600 0 196 0 196 0 36 0 1 %e A213600 196 0 784 0 400 0 49 0 1 %e A213600 0 1764 0 2304 0 729 0 64 0 1 %e A213600 1764 0 8100 0 5625 0 1225 0 81 0 1 %e A213600 ... %Y A213600 Row sums give A000108. %Y A213600 T(2n,0) gives A001246. %Y A213600 T(2n,2) gives A338727(n) for n>=1. %Y A213600 Cf. A053121. %K A213600 nonn,tabl %O A213600 0,8 %A A213600 _David Scambler_, Jun 14 2012