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 A180262 #5 Jan 28 2022 07:47:23 %S A180262 1,2,1,1,2,3,1,1,6,6,1,1,3,12,14,1,1,3,6,28,31,1,1,3,6,14,62,70,1,1,3, %T A180262 6,14,31,140,157,1,1,3,6,14,31,70,314,353,1,1,3,6,14,31,70,157,706, %U A180262 793,1,1,3,6,14,31,70,157,353,1586,1782 %N A180262 Triangle by rows, generated from a triangle with (1,2,1,1,1,...) in every column. %C A180262 Row sums = A006356: (1, 3, 6, 14, 31, 70, 157, 353,...). %C A180262 Sum of n-th row terms = rightmost term of next row. %F A180262 Let M be an infinite Toeplitz lower triangular matrix with (1,2,1,1,1,..) in every column. A180262 = M * a diagonalized variant of A006356 such that the main diagonal = A006356 prefaced with a 1: (1, 1, 3, 6, 14, 31,...) and the rest zeros. %e A180262 First few rows of the triangle: %e A180262 1; %e A180262 2, 1; %e A180262 1, 2, 3; %e A180262 1, 1, 6, 6; %e A180262 1, 1, 3, 12, 14; %e A180262 1, 1, 3, 6, 28, 31; %e A180262 1, 1, 3, 6, 14, 62, 70; %e A180262 1, 1, 3, 6, 14, 31, 140, 157; %e A180262 1, 1, 3, 6, 14, 31, 70, 314, 353; %e A180262 1, 1, 3, 6, 14, 31, 70, 157, 706, 793; %e A180262 1, 1, 3, 6, 14, 31, 70, 157, 353, 1586, 1782; %e A180262 1, 1, 3, 6, 14, 31, 70, 157, 353, 793, 3564, 4004; %e A180262 1, 1, 3, 6, 14, 31, 70, 157, 353, 793, 1782, 8008, 8997; %e A180262 1, 1, 3, 6, 14, 31, 70, 157, 353, 793, 1782, 4004, 17994, 20216; %e A180262 ... %e A180262 Example: row 3 of the triangle = (1, 1, 6, 6) = termwise products of (1, 1, 2, 1) and (1, 1, 3, 6). %Y A180262 Cf. A006356. %K A180262 nonn,tabl %O A180262 0,2 %A A180262 _Gary W. Adamson_, Aug 21 2010