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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/(1-x) - x^2/(1-x)^2 + xy*f(x,y)^2.
1

%I #3 Mar 30 2012 18:36:38

%S 1,1,1,0,2,2,-1,1,6,5,-2,-2,6,20,14,-3,-6,-4,30,70,42,-4,-10,-24,0,

%T 140,252,132,-5,-13,-48,-95,70,630,924,429,-6,-14,-66,-240,-350,588,

%U 2772,3432,1430,-7,-12,-66,-370,-1176,-1134,3696,12012,12870,4862,-8,-6,-36,-380,-2100,-5544,-2772,20592,51480,48620,16796

%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/(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 all 1's. Row sums give A086611.

%e Rows:

%e {1},

%e {1,1},

%e {0,2,2},

%e {-1,1,6,5},

%e {-2,-2,6,20,14},

%e {-3,-6,-4,30,70,42},

%e {-4,-10,-24,0,140,252,132},

%e {-5,-13,-48,-95,70,630,924,429},

%e {-6,-14,-66,-240,-350,588,2772,3432,1430},

%e {-7,-12,-66,-370,-1176,-1134,3696,12012,12870,4862}, ...

%Y Cf. A086611 (row sums), A086632.

%K sign,tabl

%O 0,5

%A _Paul D. Hanna_, Jul 24 2003