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%I #3 Mar 30 2012 18:36:38
%S 1,1,1,-1,3,3,-3,0,15,12,-3,-14,15,84,55,-1,-27,-75,168,495,273,0,-9,
%T -270,-336,1485,3003,1428,0,47,-252,-2352,-825,12012,18564,7752,0,93,
%U 525,-4032,-18315,6006,92820,116280,43263,0,69,1875,2940,-49005,-129129,129948,697680,735471,246675
%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)^3 + xy*f(x,y)^3.
%C The main diagonal gives A001764 ( C(3n,n)/(2n+1) ). First column is given by g.f: (1+x) - x^2*(1+x)^3. Antidiagonal sums result in binomial {1,1,0,...}.
%e Rows begin:
%e {1},
%e {1,1},
%e {-1,3,3},
%e {-3,0,15,12},
%e {-3,-14,15,84,55},
%e {-1,-27,-75,168,495,273},
%e {0,-9,-270,-336,1485,3003,1428},
%e {0,47,-252,-2352,-825,12012,18564,7752}, ...
%Y Cf. A086635 (row sums), A086632.
%K sign,tabl
%O 0,5
%A _Paul D. Hanna_, Jul 25 2003