%I
%S 1,2,1,3,0,1,4,4,4,1,5,10,10,0,1,6,18,24,12,6,1,7,28,49,42,
%T 21,0,1,8,40,88,104,72,24,8,1,9,54,144,216,198,108,36,0,1,10,
%U 70,220,400,460,340,160,40,10,1,11,88,319,682,946,880,550,220,55,0,1
%N Triangle T, read by rows, where row n of T equals row n of matrix (n+1)th power of triangle A112555.
%C Remarkably, the matrix logarithm (A113290) is an integer triangle. Matrix mth power of A112555 = I + m*(A112555  I) where I = identity matrix.
%F G.f.: A(x, y) = 1/(1x*y) + x*(x+2)/((1x*y)^2*(1+x+x*y)^2).
%e Triangle begins:
%e 1;
%e 2,1;
%e 3,0,1;
%e 4,4,4,1;
%e 5,10,10,0,1;
%e 6,18,24,12,6,1;
%e 7,28,49,42,21,0,1;
%e 8,40,88,104,72,24,8,1;
%e 9,54,144,216,198,108,36,0,1;
%e 10,70,220,400,460,340,160,40,10,1; ...
%o (PARI) {T(n,k)=local(x=X+X*O(X^n),y=Y+Y*O(Y^k)); polcoeff(polcoeff(1/(1x*y)+x*(x+2)/((1x*y)^2*(1+x+x*y)^2),n,X),k,Y)}
%Y Cf. A112555, A113288 (inverse), A113290 (log), A113291, A072374.
%K sign,tabl
%O 0,2
%A _Paul D. Hanna_, Oct 23 2005
