|
%I #6 Mar 30 2012 18:36:44
%S 1,1,1,-2,3,1,13,-19,7,1,-209,310,-115,15,1,7558,-11328,4315,-575,31,
%T 1,-584837,883178,-342761,46965,-2607,63,1,94047241,-142845383,
%U 56217824,-7856782,448173,-11199,127,1,-30883147262,47124630966,-18750717425,2660027115,-154716638,3969645,-46655,255,1
%N Triangular matrix, read by rows, where row n is formed from the first differences of row (n-1) of its inverse matrix square, with an appended '1' for the main diagonal.
%C Row sums are: {1,2,2,2,2,2,...}. Column 0 is A102585. Column 1 is A102586.
%F T(n, k) = [T^-2](n-1, k) - [T^-2](n-1, k-1) for n>k>0, with T(n, n)=1 for n>=0 and T(n, 0) = [T^-2](n-1, 0) for n>0.
%e Rows of matrix T begin:
%e [1],
%e [1,1],
%e [ -2,3,1],
%e [13,-19,7,1],
%e [ -209,310,-115,15,1],
%e [7558,-11328,4315,-575,31,1],
%e [ -584837,883178,-342761,46965,-2607,63,1],
%e [94047241,-142845383,56217824,-7856782,448173,-11199,127,1],...
%e and is formed from the first differences of the rows
%e of the inverse matrix square, T^(-2):
%e [1],
%e [ -2,1],
%e [13,-6,1],
%e [ -209,101,-14,1],
%e [7558,-3770,545,-30,1],
%e [ -584837,298341,-44420,2545,-62,1],...
%o (PARI) {T(n,k)=local(A=Mat(1),B);for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(j==i,B[i,j]=1,if(j==1,B[i,j]=(A^-2)[i-1,1], B[i,j]=(A^-2)[i-1,j]-(A^-2)[i-1,j-1]));));A=B);return(A[n+1,k+1])}
%Y Cf. A102585, A102586, A102225.
%K sign,tabl
%O 0,4
%A _Paul D. Hanna_, Jan 22 2005
|
