%I #3 Mar 30 2012 18:36:38
%S 1,1,1,-1,2,2,-2,-1,6,5,-1,-6,0,20,14,0,-5,-22,10,70,42,0,2,-30,-80,
%T 70,252,132,0,6,6,-165,-280,378,924,429,0,4,52,-20,-840,-924,1848,
%U 3432,1430,0,1,48,330,-406,-4032,-2772,8580,12870,4862,0,0,0,440,1750,-3528,-18480,-6864,38610,48620,16796
%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) = (1+x) - x^2*(1+x)^2 + xy*f(x,y)^2.
%C The main diagonal gives the Catalan sequence A000108. Antidiagonal sums results in binomial {1,1}. Row sums give A086613.
%e Rows:
%e {1},
%e {1,1}
%e {-1,2,2},
%e {-2,-1,6,5},
%e {-1,-6,0,20,14},
%e {0,-5,-22,10,70,42},
%e {0,2,-30,-80,70,252,132},
%e {0,6,6,-165,-280,378,924,429},
%e {0,4,52,-20,-840,-924,1848,3432,1430},
%e {0,1,48,330,-406,-4032,-2772,8580,12870,4862}, ...
%Y Cf. A086613 (row sums), A086634.
%K sign,tabl
%O 0,5
%A _Paul D. Hanna_, Jul 24 2003