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 A118024 #9 Nov 04 2024 18:16:45
%S A118024 1,1,1,2,2,1,6,8,4,1,28,48,32,8,1,216,448,384,128,16,1,2864,6912,7168,
%T A118024 3072,512,32,1,66656,183296,221184,114688,24576,2048,64,1,2760896,
%U A118024 8531968,11730944,7077888,1835008,196608,8192,128,1,205824384,706789376
%N A118024 Triangle T, read by rows, T(n,k) = T(n-k)*2^(k*(n-k)) such that column 0 of the matrix square of T equals column 0 of T shifted left: [T^2](n,k) = T(n-k+1,0)*2^(k*(n-k)) for n>=k>=0.
%C A118024 Column 0 is A118025, where T(n,k) = A118025(n-k)*2^(k*(n-k)).
%F A118024 T(n,k) = A118025(n-k)*2^(k*(n-k)) for n>=k>=0.
%e A118024 Triangle T begins:
%e A118024 1;
%e A118024 1,1;
%e A118024 2,2,1;
%e A118024 6,8,4,1;
%e A118024 28,48,32,8,1;
%e A118024 216,448,384,128,16,1;
%e A118024 2864,6912,7168,3072,512,32,1;
%e A118024 66656,183296,221184,114688,24576,2048,64,1; ...
%e A118024 2760896,8531968,11730944,7077888,1835008,196608,8192,128,1; ...
%e A118024 Matrix square is given by [T^2](n,k) = T(n-k+1,0)*2^(k*(n-k)):
%e A118024 1;
%e A118024 2,1;
%e A118024 6,4,1;
%e A118024 28,24,8,1;
%e A118024 216,224,96,16,1;
%e A118024 2864,3456,1792,384,32,1; ...
%e A118024 so that column 0 of T^2 equals column 0 of T shift left 1 place.
%o A118024 (PARI) {T(n, k)=if(n<0 || k>n,0,if(n==k,1,2^k*sum(j=0, n-1, T(n-1, j)*T(j, k)); ))} \\ _Paul D. Hanna_, Sep 25 2006
%Y A118024 Cf. A118025 (column 0); A117401 (related triangle); A118022 (variant).
%Y A118024 Cf. A123305.
%K A118024 nonn,tabl
%O A118024 0,4
%A A118024 _Paul D. Hanna_, Apr 10 2006