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.

1, 1, 1, 3, 2, 1, 14, 8, 3, 1, 85, 44, 15, 4, 1, 621, 298, 96, 24, 5, 1, 5236, 2358, 729, 176, 35, 6, 1, 49680, 21154, 6327, 1492, 290, 48, 7, 1, 521721, 211100, 61380, 14220, 2725, 444, 63, 8, 1, 5994155, 2313030, 655944, 149812, 28425, 4590, 644, 80, 9, 1

Offset: 0

Author

Paul D. Hanna, Oct 06 2005

Keywords

• nonn
• tabl

Comments

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

Examples

			Triangle T begins:
1;
1,1;
3,2,1;
14,8,3,1;
85,44,15,4,1;
621,298,96,24,5,1;
5236,2358,729,176,35,6,1;
49680,21154,6327,1492,290,48,7,1; ...
Matrix inverse T^-1 begins:
1;
-1,1;
-1,-2*1,1;
-3,-2*1,-3*1,1;
-14,-2*3,-3*1,-4*1,1;
-85,-2*14,-3*3,-4*1,-5*1,1;
-621,-2*85,-3*14,-4*3,-5*1,-6*1,1; ...
where [T^-1](n,k) = -(k+1)*T(n-1,0) for n>k>=0.
		

Crossrefs

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

Programs

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])}