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.

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, 22, 151, 370, 370, 151, 22, 1, 1, 29, 274, 952, 1419, 952, 274, 29, 1, 1, 37, 463, 2185, 4573, 4573, 2185, 463, 37, 1, 1, 46, 739, 4579, 12892, 18037, 12892, 4579, 739, 46, 1

Offset: 0

Author

Paul D. Hanna, Jul 27 2003

Keywords

• nonn
• tabl

Comments

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.

Crossrefs

Cf. A086630 (diagonal), A086631 (antidiagonal sums).

Programs

Mathematica

m = 11; f[, ] = 0;
Do[f[x_, y_] = 1/((1 - x)(1 - y)) + x y f[x, y]^3 + O[x]^m, {m}];
T =CoefficientList[# + O[y]^m, y]& /@ CoefficientList[f[x, y], x];
Table[T[[n-k+1, k]], {n, 1, m}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 15 2019 *)