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 A127742 #7 Jan 14 2013 21:48:21 %S A127742 1,1,1,2,2,1,5,4,1,3,1,14,10,4,6,3,4,1,42,28,10,4,15,12,1,8,6,5,1,132, %T A127742 84,28,20,42,30,12,6,20,24,4,10,10,6,1,429,264,84,56,25,126,84,60,15, %U A127742 12,56,60,24,24,1,25,40,10,12,15,7,1,1430,858,264,168,140,396,252,168,75 %N A127742 Triangle read by rows with shape A000041 which refines the Catalan triangle A033184 using sequence A048996. %C A127742 Contribution from _R. J. Mathar_, Jul 16 2010: (Start) %C A127742 The entries count Dyck paths of length 2n which have a step/stride pattern between consecutive returns to the horizontal axes (after sorting) equivalent to the k-th partition of n. %C A127742 Equivalent means that each distance between two x (where y=0) is divided by 2 prior to comparison. %C A127742 Example: if the x-values are (0,4,8,10,16) with 2n=16, the strides are 4,4,2,6, equal to 2,2,1,3 after division by 2, and contribute to the 1^1,2^2,3^1 partition T(8,14). (End) %e A127742 The triangle begins %e A127742 1 %e A127742 1 1 %e A127742 2 2 1 %e A127742 5 4 1 3 1 %e A127742 14 10 4 6 3 4 1 %e A127742 etc %K A127742 nonn,tabf %O A127742 1,4 %A A127742 _Alford Arnold_, Feb 23 2007 %E A127742 More terms from _R. J. Mathar_, Jul 16 2010