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 A131251 #12 Feb 18 2022 22:40:36 %S A131251 1,2,1,3,3,1,4,6,3,1,5,10,7,3,1,6,15,14,7,3,1,7,21,25,15,7,3,1,8,28, %T A131251 41,30,15,7,3,1,9,36,63,56,31,15,7,3,1,10,45,92,98,62,31,15,7,3,1 %N A131251 A000012 * A052509. %C A131251 Row sums = A001924: (1, 3, 7, 14, 26, 46, 79, ...). A131252 = A052509 * A000012. %C A131251 From _Clark Kimberling_, Feb 07 2011: (Start) %C A131251 When formatted as a rectangle R with northwest corner %C A131251 1, 2, 3, 4, 5, 6, ... %C A131251 1, 3, 6, 10, 15, 21, ... %C A131251 1, 3, 7, 14, 25, 41, ... %C A131251 1, 3, 7, 15, 30, 56, ... %C A131251 1, 3, 7, 15, 31, 62, ... %C A131251 ... %C A131251 the following properties hold: %C A131251 R is the accumulation array of the transpose of A052553 (a version of Pascal's triangle); see A144112 for the definition of accumulation array. %C A131251 row 1: A000027 %C A131251 row 2: A000217 %C A131251 row 3: A004006 %C A131251 row 4: A055795 %C A131251 row 5: A057703 %C A131251 row 6: A115567 %C A131251 limiting row: A000225 %C A131251 antidiagonal sums: A001924. %C A131251 (End) %F A131251 A000012 * A052509 as infinite lower triangular matrices. %e A131251 First few rows of the triangle: %e A131251 1; %e A131251 2, 1; %e A131251 3, 3, 1; %e A131251 4, 6, 3, 1; %e A131251 5, 10, 7, 3, 1; %e A131251 6, 15, 14, 7, 3, 1; %e A131251 7, 21, 25, 15, 7, 3, 1; %e A131251 ... %Y A131251 Cf. A052509, A000012, A001924, A131252. %K A131251 nonn,tabl %O A131251 0,2 %A A131251 _Gary W. Adamson_, Jun 23 2007