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 A143774 #9 Nov 20 2022 10:52:56 %S A143774 1,1,1,1,3,2,1,7,14,6,1,15,70,70,28,1,31,310,930,868,204,1,63,1302, %T A143774 8370,18228,12852,2344 %N A143774 Eigentriangle of triangle A022166. %C A143774 An eigentriangle of triangle T may be defined by taking the termwise product of row n-1 of T and the first n terms of the eigensequence of T; 0<=k<=n. %C A143774 Row sums = A125812 shifted 1 place to the left: (1, 2, 6, 28, 204,...). %C A143774 Sum of n-th row terms = rightmost term of (n+1)-th row. %C A143774 1, 1; %C A143774 1, 3, 1; %C A143774 1, 7, 7, 1; %C A143774 1, 15, 35, 15, 1; %C A143774 ... (and the eigensequence of A022166 = A125812: (1, 1, 2, 6, 28, 204,...) we apply the termwise product of (n-1)-th row of A022166 and the first n terms of A125812. %F A143774 Given triangle A022166: 1; %e A143774 First few rows of the triangle: %e A143774 1; %e A143774 1, 1; %e A143774 1, 3, 2; %e A143774 1, 7, 14, 6; %e A143774 1, 15, 70, 90, 28; %e A143774 1, 31, 310, 930, 868, 204; %e A143774 ... %e A143774 Row 3 of A022166 = (1, 7, 7, 1), first 4 terms of A143774 = (1, 1, 2, 6), so row 3 of A143774 = (1*1, 7*1, 7*2, 1*6) = (1, 7, 14, 6). %Y A143774 Cf. A022166, A125812. %K A143774 nonn,tabl,more %O A143774 0,5 %A A143774 _Gary W. Adamson_, Aug 31 2008