Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Jun 19 2024 09:33:21
%S 1,2,2,2,0,4,4,0,-4,8,12,0,8,-32,8,48
%N A finite irregular triangle.
%F 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 The finite triangle, T(n,k), is:
%e 1;
%e 2;
%e 2, 2;
%e 0, 4, 4;
%e 0, -4, 8, 12;
%e 0, 8, -32, 8, 48;
%t 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 Table[CoefficientList[Apply[Plus, t[[m]]], n], {m,Length[t]}]//Flatten
%K sign,tabf,fini,full,less
%O 0,2
%A _Roger L. Bagula_, Jan 20 2009
%E Edited by _G. C. Greubel_, Jun 18 2024