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 A144962 #4 Jun 02 2025 00:37:09 %S A144962 1,1,1,1,1,2,3,1,2,4,5,3,2,4,10,17,5,6,4,10,24,41,17,10,12,10,24,66, %T A144962 127,41,34,20,30,24,66,180,365,127,82,68,50,72,66,180,522,1119,365, %U A144962 254,164,170,120,198,180,522,1532 %N A144962 Eigentriangle, row sums = A000084. %C A144962 Row sums = A000084: (1, 2, 4, 10, 24, 66,...). %C A144962 Right border = A000084 shifted: (1, 1, 2, 4, 10, 24,...) %C A144962 Left border = A001572: (1, 1, 1, 3, 5, 17, 41,...). %C A144962 A000084 = the INVERT transform of A001572. %C A144962 Sum of n-th row terms = rightmost term of next row. %F A144962 Triangle read by rows, T(n,k) = A001572(n-k+1) * (A000084 * 0^(n-k)), 1<=k<=n. %F A144962 Given an A001572 "decrescendo" triangle: (1; 1,1; 1,1,1; 3,1,1,1; 5,3,1,1,1;...), where A001572 begins: (1, 1, 1, 3, 5, 17, 41, 127,...); apply termwise products of the decrescendo triangle row terms to A000084 terms: (1, 2, 4, 10, 24, 66, 180, 522,...). %e A144962 First few rows of the triangle = %e A144962 1; %e A144962 1, 1; %e A144962 1, 1, 2; %e A144962 3, 1, 2, 4; %e A144962 5, 3, 2, 4, 10; %e A144962 17, 5, 6, 4, 10, 24; %e A144962 41, 17, 10, 12, 10, 24, 66; %e A144962 127, 41, 34, 20, 30, 24, 66, 180; %e A144962 365, 127, 82, 68, 50, 72, 66, 180, 522; %e A144962 1119, 365, 254, 164, 170, 120, 198, 180, 522, 1532; %e A144962 ... %e A144962 Example: row 5 = (5, 3, 2, 4, 10) = termwise products of (5, 3, 1, 1, 1) and (1, 1, 2, 4, 10). %Y A144962 A000084, Cf. A001572 %K A144962 nonn,tabl %O A144962 1,6 %A A144962 _Gary W. Adamson_, Sep 27 2008