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 A174740 #33 Jan 12 2023 01:34:22 %S A174740 1,1,2,2,2,0,3,4,0,0,5,6,0,0,-5,7,10,0,0,-5,0,11,14,0,0,-10,0,-7,15, %T A174740 22,0,0,-15,0,-7,0,22,30,0,0,-25,0,-14,0,0,30,44,0,0,-35,0,-21,0,0,0, %U A174740 42,60,0,0,-55,0,-35,0,0,0,0,56,84,0,0,-75,0,-49,0,0,0,0,12 %N A174740 Triangle read by rows, A027293 * an infinite lower triangular matrix with A147843 as the diagonal and the rest zeros. %C A174740 Left border = the partition numbers, A000041; right border = A147843 starting (1, 2, 0, ...). %C A174740 Row sums apparently give A000203. Check: Sum of row 6 terms = [7, 5, 3, 2, 1, 1] dot [1, 2, 0, 0, -5, 0] = [7 + 10 + 0 + 0 -5 + 0] = 12 = A000203(6). %F A174740 Equals triangle A027293 * a lower triangular matrix with A147843 (deleting the first zero) as the right border and the rest zeros. %F A174740 T(n,k) = A147843(k) * A027293(n,k). - _Joerg Arndt_, Dec 29 2022 %e A174740 First few rows of the triangle: %e A174740 1; %e A174740 1, 2; %e A174740 2, 2, 0; %e A174740 3, 4, 0, 0; %e A174740 5, 6, 0, 0, -5; %e A174740 7, 10, 0, 0, -5, 0; %e A174740 11, 14, 0, 0, -10, 0, -7; %e A174740 15, 22, 0, 0, -15, 0, -7, 0; %e A174740 22, 30, 0, 0, -25, 0, -14, 0, 0; %e A174740 30, 44, 0, 0, -35, 0, -21, 0, 0, 0; %e A174740 42, 60, 0, 0, -55, 0, -35, 0, 0, 0, 0; %e A174740 56, 84, 6, 0, -75, 0, -49, 0, 0, 0, 0, 12; %e A174740 ... %Y A174740 Cf. A027293, A147843, A000041, A000203. %K A174740 tabl,sign %O A174740 1,3 %A A174740 _Gary W. Adamson_, Mar 28 2010 %E A174740 Terms corrected by _Gary W. Adamson_, Dec 27 2022