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.
Triangle T begins: 1; 1, 1; 4, 2, 1; 28, 10, 3, 1; 268, 78, 18, 4, 1; 3164, 798, 156, 28, 5, 1; 43672, 9874, 1714, 268, 40, 6, 1; 682632, 141282, 22368, 3164, 420, 54, 7, 1; 11834536, 2273730, 333910, 43672, 5320, 618, 70, 8, 1; 224283416, 40400466, 5566728, 682632, 77720, 8378, 868, 88, 9, 1; ... where column k of T = column 0 of T^(k+1) with column 0 of T = column 0 of T^4 shift right: column 1 of T = column 0 of T^2; column 2 of T = column 0 of T^3; column 3 of T = column 0 of T^4. Matrix square of T, T^2, begins: 1; 2, 1; 10, 4, 1; 78, 26, 6, 1; 798, 232, 48, 8, 1; 9874, 2578, 486, 76, 10, 1; 141282, 33764, 5888, 864, 110, 12, 1; 2273730, 503910, 82210, 11396, 1390, 150, 14, 1; ... where column k of T^2 = column 1 of T^(k+1): column 0 of T^2 = column 1 of T; column 2 of T^2 = column 1 of T^3; column 3 of T^2 = column 1 of T^4. Matrix cube of T, T^3, begins: 1; 3, 1; 18, 6, 1; 156, 48, 9, 1; 1714, 486, 90, 12, 1; 22368, 5888, 1050, 144, 15, 1; 333910, 82210, 14046, 1908, 210, 18, 1; 5566728, 1289928, 211182, 28072, 3120, 288, 21, 1; ... where column k of T^3 = column 2 of T^(k+1): column 0 of T^3 = column 2 of T; column 1 of T^3 = column 2 of T^2; column 3 of T^3 = column 2 of T^4. Matrix 4th power of T, T^4, begins: 1; 4, 1; 28, 8, 1; 268, 76, 12, 1; 3164, 864, 144, 16, 1; 43672, 11396, 1908, 232, 20, 1; 682632, 170000, 28072, 3520, 340, 24, 1; 11834536, 2814832, 454848, 57408, 5820, 468, 28, 1; ... where column k of T^4 = column 3 of T^(k+1): column 0 of T^4 = column 3 of T = column 0 of T shift left; column 1 of T^4 = column 3 of T^2; column 2 of T^4 = column 3 of T^3.
{T(n, k) = if(k>n||k<0, 0, if(k==n, 1, if(k==0, T(n+2, 3), sum(j=0, n-k, T(n-k, j)*T(j+k-1, k-1))); ); )}
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
/* Column k of T = column 0 of T^(k+1): */
{T(n, k) = local(M=if(n==0,Mat(1),matrix(n,n,r,c,if(r>=c,T(r-1,c-1))))); if(k==n, 1, if(k==0, (M^4)[n, 1],(M^(k+1))[n-k+1, 1]))}
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))