A112911 - OEIS

%I #3 Mar 30 2012 18:36:51

%S 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 176,35,6,1,49680,21154,6327,1492,290,48,7,1,521721,211100,61380,

%U 14220,2725,444,63,8,1,5994155,2313030,655944,149812,28425,4590,644,80,9,1

%N 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 Matrix inverse square satisfies: [T^-2](3*n+2,n) = 0 for n>=0.

%e Triangle T begins:

%e 1;

%e 1,1;

%e 3,2,1;

%e 14,8,3,1;

%e 85,44,15,4,1;

%e 621,298,96,24,5,1;

%e 5236,2358,729,176,35,6,1;

%e 49680,21154,6327,1492,290,48,7,1; ...

%e Matrix inverse T^-1 begins:

%e 1;

%e -1,1;

%e -1,-2*1,1;

%e -3,-2*1,-3*1,1;

%e -14,-2*3,-3*1,-4*1,1;

%e -85,-2*14,-3*3,-4*1,-5*1,1;

%e -621,-2*85,-3*14,-4*3,-5*1,-6*1,1; ...

%e where [T^-1](n,k) = -(k+1)*T(n-1,0) for n>k>=0.

%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,B[i,j]=-j*(A^-1)[i-j,1] );));A=B);return((A^-1)[n+1,k+1])}

%Y Cf. A088716 (column 0), A112912 (column 1), A112913 (column 2), A112914 (column 3).

%K nonn,tabl

%O 0,4

%A _Paul D. Hanna_, Oct 06 2005