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 A153585 #5 Jun 02 2025 01:17:29 %S A153585 1,0,1,1,0,2,0,2,0,3,2,0,6,0,6,0,5,0,12,0,10,5,0,18,0,30,0,20,0,14,0, %T A153585 42,0,60,0,35,14,0,56,0,120,0,140,0,70,0,42,0,144,0,270,0,280,0,126 %N A153585 Convolution triangle, A053121 * (A001405 * 0^(n-k)). %C A153585 Row sums = A145974: (1, 1, 3, 5, 14, 27, 73,...). %F A153585 Convolution triangle, A053121 * (A001405 * 0^(n-k)). %F A153585 A053121 = the aerated Catalan triangle and (A001405 * 0^(n-k) = an %F A153585 infinite lower triangular matrix with A001405 as the main diagonal and %F A153585 the rest zeros. %e A153585 First few rows of the triangle = %e A153585 1; %e A153585 0, 1; %e A153585 1, 0, 2; %e A153585 0, 2, 0, 3; %e A153585 2, 0, 6, 0, 6; %e A153585 0, 5, 0, 12, 0, 10; %e A153585 5, 0, 18, 0, 30, 0, 20; %e A153585 0, 14, 0, 42, 0, 60, 0, 35; %e A153585 14, 0, 56, 0, 120, 0, 140, 0, 70; %e A153585 0, 42, 0, 144, 0, 270, 0, 280, 0, 126; %e A153585 42, 0, 180, 0, 450, 0, 700, 0, 630, 0, 252; %e A153585 ... %e A153585 Example: Row 4 = (2, 0, 6, 0, 6) = termwise products of (2, 0, 3, 0, 1) and (1, 1, 2, 3, 6). %K A153585 nonn,tabl %O A153585 0,6 %A A153585 _Gary W. Adamson_, Dec 28 2008