%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/(1x*y)+x/((1x*y)*(1+x+x*y)),r1,X),c1,Y))))); if(n<k,0,(sum(j=1,n+1,(M^0M)^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
