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 A155123 #17 Jun 19 2024 09:33:21
%S A155123 1,2,2,2,0,4,4,0,-4,8,12,0,8,-32,8,48
%N A155123 A finite irregular triangle.
%F A155123 T(n, k) = [x^k]( p(n, x) ), where p(0,x) = 1, p(1,x) = 2, p(2,x) = 2*x + 2, p(3,x) = 4*x^2 + 4*x, p(4,x) = 12*x^3 + 8*x^2 - 4*x, and p(5,x) = 48*x^4 + 8*x^3 - 32*x^2 + 8*x.
%e A155123 The finite triangle, T(n,k), is:
%e A155123 1;
%e A155123 2;
%e A155123 2, 2;
%e A155123 0, 4, 4;
%e A155123 0, -4, 8, 12;
%e A155123 0, 8, -32, 8, 48;
%t A155123 t = {{1}, {1,1}, {1, 2*n, 1}, {1, -1 +2*n +2*n^2, -1 +2*n +2*n^2, 1}, {1, -2 +2*n +2*n^2 +2*n^3, 2 -8*n +4*n^2 +8*n^3, -2 +2*n +2*n^2 +2*n^3, 1}, {1, -3 +2*n +2*n^2 +2*n^3 +2*n^4, 2 +2*n -18*n^2 +2*n^3 +22*n^4, 2 +2*n - 18*n^2 +2*n^3 +22*n^4, -3 +2*n +2*n^2 +2*n^3 +2*n^4, 1}};
%t A155123 Table[CoefficientList[Apply[Plus, t[[m]]], n], {m,Length[t]}]//Flatten
%K A155123 sign,tabf,fini,full,less
%O A155123 0,2
%A A155123 _Roger L. Bagula_, Jan 20 2009
%E A155123 Edited by _G. C. Greubel_, Jun 18 2024