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%I #5 Mar 30 2012 18:36:51
%S 1,-2,1,3,0,1,-8,-4,-4,1,15,10,10,0,1,-36,-30,-36,-12,-6,1,77,70,91,
%T 42,21,0,1,-192,-184,-256,-152,-96,-24,-8,1,459,450,648,432,306,108,
%U 36,0,1,-1220,-1210,-1780,-1280,-1000,-460,-200,-40,-10,1,3201,3190,4741,3542,2926,1540,770,220,55,0,1
%N Matrix inverse of triangle A113287.
%F T(n, 0) = (-1)^n*(n+1)*A072374(n-1) for n>=2, with T(1, 0)=-2, T(n, n)=1. T(n, 1) = (-1)^n*(n+1)*(A072374(n-1) - 1) for n>=2.
%e Triangle begins:
%e .1;
%e .-2,1;
%e .3,0,1;
%e .-8,-4,-4,1;
%e .15,10,10,0,1;
%e .-36,-30,-36,-12,-6,1;
%e .77,70,91,42,21,0,1;
%e .-192,-184,-256,-152,-96,-24,-8,1;
%e .459,450,648,432,306,108,36,0,1;
%e .-1220,-1210,-1780,-1280,-1000,-460,-200,-40,-10,1;
%e .3201,3190,4741,3542,2926,1540,770,220,55,0,1; ...
%o (PARI) {T(n,k)=local(x=X+O(X^(n+2)),y=Y+O(Y^(n+2)),M=matrix(n+1,n+1,r,c, polcoeff(polcoeff(1/(1-x*y)+r*x/((1-x*y)*(1+x+x*y)),r-1,X),c-1,Y))); if(n<k,0,(M^-1)[n+1,k+1])}
%Y Cf. A113287, A113289 (row sums), A113290 (-log), A072374.
%K sign,tabl
%O 0,2
%A _Paul D. Hanna_, Oct 23 2005
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