%I #3 Mar 30 2012 18:36:38
%S 1,1,1,1,3,3,2,6,15,12,5,13,45,84,55,14,33,120,336,495,273,42,93,330,
%T 1092,2475,3003,1428,132,280,963,3360,9570,18018,18564,7752,429,882,
%U 2955,10416,33165,81081,129948,116280,43263,1430,2871,9420,33096,110880
%N Triangle of coefficients, read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (3-sqrt(1-4x))/2 + xy*f(x,y)^3.
%C The main diagonal is A001764 ( C(3n,n)/(2n+1) ). First column is the Catalan sequence A000108, offset by 1. Antidiagonal sums also results in the Catalan sequence A000108.
%e Rows begin:
%e {1},
%e {1,1},
%e {1,3,3},
%e {2,6,15,12},
%e {5,13,45,84,55},
%e {14,33,120,336,495,273},
%e {42,93,330,1092,2475,3003,1428},
%e {132,280,963,3360,9570,18018,18564,7752},
%e {429,882,2955,10416,33165,81081,129948,116280,43263}, ...
%Y Cf. A086637 (row sums), A001764, A000108 (Catalan).
%K nonn,tabl
%O 0,5
%A _Paul D. Hanna_, Jul 24 2003