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.
This triangle begins: 1; 1, 2; 1, 3, 9; 1, 4, 14, 32; 1, 5, 20, 55, 140; 1, 6, 27, 86, 243, 630; 1, 7, 35, 126, 392, 1099, 2870; 1, 8, 44, 176, 598, 1808, 5048, 13256; ... The g.f. A(x) of this sequence as a flat list of coefficients begins: A(x) = 1 + x + 2*x^2 + x^3 + 3*x^4 + 9*x^5 + x^6 + 4*x^7 + 14*x^8 + 32*x^9 + x^10 + 5*x^11 + 20*x^12 + 55*x^13 + 140*x^14 +... such that the coefficients in A(x)^n, n>=1, forms the table: A^1: [(1),1, 2, 1, 3, 9, 1, 4, 14, 32, ...]; A^2: [(1, 2), 5, 6, 12, 28, 33, 52, 67, 164, ...]; A^3: [(1, 3, 9), 16, 33, 72, 125, 222, 330, 646, ...]; A^4: [(1, 4, 14, 32), 73, 164, 334, 660, 1152, 2184, ...]; A^5: [(1, 5, 20, 55, 140), 336, 755, 1625, 3195, 6315, ...]; A^6: [(1, 6, 27, 86, 243, 630),1532, 3546, 7635, 16020, ...]; A^7: [(1, 7, 35, 126, 392, 1099, 2870), 7092, 16443, 36666, ...]; A^8: [(1, 8, 44, 176, 598, 1808, 5048, 13256),32761, 77384, ...]; A^9: [(1, 9, 54, 237, 873, 2835, 8433, 23454, 61389),153007, ...]; ... where the lower triangular portion equals this sequence.
/* As a flattened triangle: */
{a(n)=local(t=(sqrt(8*n+1)+1)\2,A=1+sum(k=1,min(n-1,t),a(k)*x^k));if(n==0,1,polcoeff((A+x*O(x^n))^t,n-t*(t-1)/2))}
for(n=0,60,print1(a(n),", "))