cp's OEIS Frontend

A086629 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/[(1-x)(1-y)] + xy*f(x,y)^3.

%I A086629 #7 Nov 15 2019 17:41:54
%S A086629 1,1,1,1,2,1,1,4,4,1,1,7,13,7,1,1,11,34,34,11,1,1,16,76,124,76,16,1,1,
%T A086629 22,151,370,370,151,22,1,1,29,274,952,1419,952,274,29,1,1,37,463,2185,
%U A086629 4573,4573,2185,463,37,1,1,46,739,4579,12892,18037,12892,4579,739,46,1
%N A086629 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/[(1-x)(1-y)] + xy*f(x,y)^3.
%C A086629 If 1 is subtracted from every element of the table, the resulting table forms the coefficients of f(x,y)^3, where f(x,y) = 1/[(1-x)(1-y)] + xy*f(x,y)^3.
%t A086629 m = 11; f[_, _] = 0;
%t A086629 Do[f[x_, y_] = 1/((1 - x)(1 - y)) + x y f[x, y]^3 + O[x]^m, {m}];
%t A086629 T =CoefficientList[# + O[y]^m, y]& /@ CoefficientList[f[x, y], x];
%t A086629 Table[T[[n-k+1, k]], {n, 1, m}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Nov 15 2019 *)
%Y A086629 Cf. A086630 (diagonal), A086631 (antidiagonal sums).
%K A086629 nonn,tabl
%O A086629 0,5
%A A086629 _Paul D. Hanna_, Jul 27 2003