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 A144032 #11 Feb 01 2025 08:47:17 %S A144032 1,0,1,-1,0,1,-1,-1,0,0,-2,-1,-1,0,-2,-1,-2,-1,0,0,-6,-2,-1,-2,0,2,0, %T A144032 -10,-2,-2,-1,0,2,6,0,-13,-2,-2,-2,0,46,10,0,-10,-1,-2,-2,0,2,12,10, %U A144032 13,0,4,-2,-1,-2,0,4,6,10,13,10,0,36,-2,-2,-1,0,4,12,10,26,10,-4,0,84,-3 %N A144032 Triangle read by rows: T(n,k) = A002321(n-k+1)*A144031(k-1). %C A144032 Row sums = A144031, the INVERT transform of A002321. %C A144032 Left border = the Mertens's function, A002321. %C A144032 Right border = A144031 shifted. %C A144032 Sum of n-th row terms = rightmost term of (n+1)-th row. %e A144032 First few rows of the triangle: %e A144032 1; %e A144032 0, 1; %e A144032 -1, 0, 1; %e A144032 -1, -1, 0, 0; %e A144032 -2, -1, -1, 0, -2; %e A144032 -1, -2, -1, 0, 0, -6; %e A144032 -2, -1, -2, 0, 2, 0, -10; %e A144032 -2, -2, -1, 0, 2, 6, 0, -13; %e A144032 -2, -2, -2, 0, 4, 6, 10, 0, -10; %e A144032 ... %e A144032 Row 5 = (-2, -1, -1, 0, -2) termwise products of (-2, -1, -1, 0, 1) and (1, 1, 1, 0, -2); = ((-2)*(1), (-1)*(1), (-1)*(1), (0)*(0), (1)*(-2)). (-2, -1, -1, 0, 1) = the first 5 terms of A002321, the Mertens's function. (1, 1, 1, 0, -2) = 5 shifted terms of A144031. %Y A144032 Cf. A002321, A144031. %K A144032 tabl,sign %O A144032 1,11 %A A144032 _Gary W. Adamson_, Sep 07 2008