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A113290 Matrix logarithm of triangle A113287. 5

%I #4 Mar 30 2012 18:36:51

%S 0,2,0,-3,0,0,6,4,4,0,-10,-10,-10,0,0,19,24,30,12,6,0,-35,-49,-70,-42,

%T -21,0,0,72,104,164,128,84,24,8,0,-150,-216,-360,-324,-252,-108,-36,0,

%U 0,343,480,820,800,710,400,180,40,10,0,-803,-1089,-1870,-1892,-1826,-1210,-660,-220,-55,0,0

%N Matrix logarithm of triangle A113287.

%F T(n, 1) = (n+1)*A113291(n).

%e Triangle begins:

%e 0;

%e 2,0;

%e -3,0,0;

%e 6,4,4,0;

%e -10,-10,-10,0,0;

%e 19,24,30,12,6,0;

%e -35,-49,-70,-42,-21,0,0;

%e 72,104,164,128,84,24,8,0;

%e -150,-216,-360,-324,-252,-108,-36,0,0;

%e 343,480,820,800,710,400,180,40,10,0; ...

%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,if(r==c,1, if(r>c,r*polcoeff(polcoeff(1/(1-x*y)+x/((1-x*y)*(1+x+x*y)),r-1,X),c-1,Y))))); if(n<k,0,(sum(j=1,n+1,-(M^0-M)^j/j))[n+1,k+1])}

%Y Cf. A113287, A113288, A113291 (column 1), A113292 (column 0), A072374.

%K sign,tabl

%O 0,2

%A _Paul D. Hanna_, Oct 23 2005

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