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 A086623 #3 Mar 30 2012 18:36:38 %S A086623 1,1,1,1,1,1,1,2,2,1,1,3,4,3,1,1,4,8,8,4,1,1,5,14,19,14,5,1,1,6,22,40, %T A086623 40,22,6,1,1,7,32,76,100,76,32,7,1,1,8,44,132,222,222,132,44,8,1,1,9, %U A086623 58,213,448,570,448,213,58,9,1,1,10,74,324,834,1316,1316,834,324,74,10,1,1 %N A086623 Symmetric square table of coefficients, read by antidiagonals, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1-xy)/[(1-x)(1-y)] + xy*f(x,y)^2. %C A086623 The first row and column of 1's together form: (1-xy)/[(1-x)(1-y)], while the remaining square table (excluding the first row and column) give the coefficients of f(x,y)^2. %e A086623 Rows begin: %e A086623 1,1,_1,__1,___1,___1,____1,____1,_____1, ... %e A086623 1,1,_2,__3,___4,___5,____6,____7,_____8, ... %e A086623 1,2,_4,__8,__14,__22,___32,___44,____58, ... %e A086623 1,3,_8,_19,__40,__76,__132,__213,___324, ... %e A086623 1,4,14,_40,_100,_222,__448,__834,__1450, ... %e A086623 1,5,22,_76,_222,_570,_1316,_2782,__5458, ... %e A086623 1,6,32,132,_448,1316,_3442,_8180,_17928, ... %e A086623 1,7,44,213,-834,2782,_8180,21685,_52694, ... %e A086623 1,8,58,324,1450,5458,17928,52694,141112, ... %Y A086623 Cf. A086624 (diagonal), A086625 (antidiagonal sums). %K A086623 nonn,tabl %O A086623 0,8 %A A086623 _Paul D. Hanna_, Jul 24 2003