cp's OEIS Frontend

A112911 Triangle T, read by rows, such that the matrix inverse satisfies: [T^-1](n,k) = -(k+1)*T(n-1,0) for n>k>=0, with T(n,n)=1 for n>=0.

%I A112911 #3 Mar 30 2012 18:36:51
%S A112911 1,1,1,3,2,1,14,8,3,1,85,44,15,4,1,621,298,96,24,5,1,5236,2358,729,
%T A112911 176,35,6,1,49680,21154,6327,1492,290,48,7,1,521721,211100,61380,
%U A112911 14220,2725,444,63,8,1,5994155,2313030,655944,149812,28425,4590,644,80,9,1
%N A112911 Triangle T, read by rows, such that the matrix inverse satisfies: [T^-1](n,k) = -(k+1)*T(n-1,0) for n>k>=0, with T(n,n)=1 for n>=0.
%C A112911 Matrix inverse square satisfies: [T^-2](3*n+2,n) = 0 for n>=0.
%e A112911 Triangle T begins:
%e A112911 1;
%e A112911 1,1;
%e A112911 3,2,1;
%e A112911 14,8,3,1;
%e A112911 85,44,15,4,1;
%e A112911 621,298,96,24,5,1;
%e A112911 5236,2358,729,176,35,6,1;
%e A112911 49680,21154,6327,1492,290,48,7,1; ...
%e A112911 Matrix inverse T^-1 begins:
%e A112911 1;
%e A112911 -1,1;
%e A112911 -1,-2*1,1;
%e A112911 -3,-2*1,-3*1,1;
%e A112911 -14,-2*3,-3*1,-4*1,1;
%e A112911 -85,-2*14,-3*3,-4*1,-5*1,1;
%e A112911 -621,-2*85,-3*14,-4*3,-5*1,-6*1,1; ...
%e A112911 where [T^-1](n,k) = -(k+1)*T(n-1,0) for n>k>=0.
%o A112911 (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,B[i,j]=-j*(A^-1)[i-j,1] );));A=B);return((A^-1)[n+1,k+1])}
%Y A112911 Cf. A088716 (column 0), A112912 (column 1), A112913 (column 2), A112914 (column 3).
%K A112911 nonn,tabl
%O A112911 0,4
%A A112911 _Paul D. Hanna_, Oct 06 2005