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 A175012 #7 Jul 20 2017 01:53:44 %S A175012 1,2,2,3,2,4,4,2,4,9,5,2,4,10,14,6,2,4,10,19,23,7,2,4,10,20,34,32,8,2, %T A175012 4,10,20,39,55,46,9,2,4,10,20,40,66,88,60,10 %N A175012 Triangle generated from the g.f of A000712 (i.e., 1/(1-x^m)^2) interleaved with zeros. %C A175012 Row sums of the triangle = A000712. %F A175012 Given 1/(1-x^m)^2 = S(x) = (1 + 2x + 3x^2 + ...), let a = S(x), b = S(x^2) (i.e., S(x) interleaved with one zero); S(x^3) = S(x) interleaved with two zeros = c, etc.; then row 1 = a, row 2 = a*b, row 3 = a*b*c, ... %F A175012 Take finite differences of the array from the top down, becoming rows of the triangle. %e A175012 First few rows of the array = %e A175012 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... %e A175012 1, 2, 5, 8, 14, 20, 30, 40, 55, 70, ... %e A175012 1, 2, 5, 10, 18, 30, 49, 74, 110, 158, ... %e A175012 1, 2, 5, 10, 20, 34, 59, 94, 149, 224, ... %e A175012 1, 2, 5, 10, 20, 36, 63, 104, 169, 264, ... %e A175012 1, 2, 5, 10, 20, 36, 65, 108, 179, 284, ... %e A175012 ... %e A175012 First few rows of the triangle = %e A175012 1; %e A175012 2; %e A175012 2, 3; %e A175012 2, 4, 4; %e A175012 2, 4, 9, 5; %e A175012 2, 4, 10, 14, 6; %e A175012 2, 4, 10, 19, 23, 7; %e A175012 2, 4, 10, 20, 34, 32, 8; %e A175012 2, 4, 10, 20, 39, 55, 46, 9; %e A175012 2, 4, 10, 20, 40, 66, 88, 60, 10; %e A175012 ... %Y A175012 Cf. A000712. %K A175012 nonn,tabl,more %O A175012 0,2 %A A175012 _Gary W. Adamson_, Apr 03 2010