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 A165194 #4 Apr 08 2022 15:24:37 %S A165194 1,1,1,1,1,2,1,1,1,2,1,2,5,2,1,1,1,2,1,2,5,2,1,1,2,5,15,5,2,5,2,1 %N A165194 Triangle of 2^n terms by rows, left half of (n+1)-th row = row n; right half = "reverse and increment" row n; using terms in A000110. %C A165194 Row sums = A000110, the Bell sequence starting with offset 1; (1, 2, 5, 15,...). %C A165194 Rows tend to A165195. %F A165194 Given the Bell sequence, A000110: (1, 1, 2, 5, 15,...); row 1 = 1, row 2 = %F A165194 (1, 1);...where left half of row (n+1) = row n. Right half of row (n+1) %F A165194 = reversal of row n, replacing terms with the next Bell number. %e A165194 First few rows of the triangle = %e A165194 1; %e A165194 1, 1; %e A165194 1, 1, 2, 1; %e A165194 1, 1, 2, 1, 2, 5, 2, 1; %e A165194 1, 1, 2, 1, 2, 5, 2, 1, 2, 5, 15, 5, 2, 5, 2, 1; %e A165194 ... %e A165194 For example: row 4, left half = (1, 1, 2, 1); right half = (1, 2, 1, 1) %e A165194 replaced with the next higher Bell numbers: (2, 5, 2, 1). Appending the two \kQ halves, we obtain row 4: (1, 1, 2, 1, 2, 5, 2, 1), sum = 15 = A000110(4). %Y A165194 A000110, A165195, A165196 %K A165194 nonn,tabf %O A165194 1,6 %A A165194 _Gary W. Adamson_, Sep 06 2009