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 A137940 #15 Apr 02 2022 14:21:39 %S A137940 1,1,1,1,2,1,1,2,4,1,1,2,5,7,1,1,2,5,13,11,1,1,2,5,14,31,16,1,1,2,5, %T A137940 14,41,66,22,1,1,2,5,14,42,116,127,29,1,1,2,5,14,42,131,302,225,37,1, %U A137940 1,2,5,14,42,132,407,715,373,46,1,1,2,5,14,42,132,428,1205,1549,586,56,1 %N A137940 Triangle read by rows, antidiagonals of an array formed by A000012 * A001263 (transform). %C A137940 Rows of the array tend to the Catalan sequence, A000108 starting (1, 2, 5, 14, 42, ...). %H A137940 Antonio Bernini, Matteo Cervetti, Luca Ferrari, Einar Steingrimsson, <a href="https://arxiv.org/abs/1910.00299">Enumerative combinatorics of intervals in the Dyck pattern poset</a>, arXiv:1910.00299 [math.CO], 2019. See Table 1 p. 4. %F A137940 Antidiagonals of an array formed by A000012 * A001263(transform), as infinite triangular matrices. A000012 = (1; 1,1; 1,1,1; 1,1,1,1; ...), A001263 = the Narayana triangle. %e A137940 First few rows of the array: %e A137940 1, 1, 1, 1, 1, ... %e A137940 1, 2, 4, 7, 11, ... %e A137940 1, 2, 5, 13, 31, ... %e A137940 1, 2, 5, 14, 41, ... %e A137940 1, 2, 5, 14, 42, ... %e A137940 ... %e A137940 First few rows of the triangle: %e A137940 1; %e A137940 1, 1; %e A137940 1, 2, 1; %e A137940 1, 2, 4, 1; %e A137940 1, 2, 5, 7, 1; %e A137940 1, 2, 5, 13, 11, 1; %e A137940 1, 2, 5, 14, 31, 16, 1; %e A137940 1, 2, 5, 14, 41, 66, 22, 1; %e A137940 1, 2, 5, 14, 42, 116, 127, 29, 1; %e A137940 1, 2, 5, 14, 42, 131, 302, 225, 37, 1; %e A137940 1, 2, 5, 14, 42, 132, 407, 715, 373, 46, 1; %e A137940 ... %Y A137940 Cf. A001263, A000108, A106396. %K A137940 nonn,tabl %O A137940 1,5 %A A137940 _Gary W. Adamson_, Feb 24 2008 %E A137940 More terms from _Alois P. Heinz_, Nov 28 2021