A107670 Matrix square of triangle A107667.

1, 12, 4, 216, 45, 9, 5248, 816, 112, 16, 160675, 20225, 2200, 225, 25, 5931540, 632700, 58176, 4860, 396, 36, 256182290, 23836540, 1920163, 138817, 9408, 637, 49, 12665445248, 1048592640, 75683648, 4886464, 290816, 16576, 960, 64

Offset: 0

Author

Paul D. Hanna, Jun 07 2005

Keywords

• nonn
• tabl

Comments

Column 0 is A006689. See triangle A107667 for more formulas.

Examples

			Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
          1;
         12,        4;
        216,       45,       9;
       5248,      816,     112,     16;
     160675,    20225,    2200,    225,   25;
    5931540,   632700,   58176,   4860,  396,  36;
  256182290, 23836540, 1920163, 138817, 9408, 637, 49;
  ...
		

Crossrefs

Cf. A107667, A107668, A107669, A006689 (column 0).

Programs

PARI

{T(n,k)=local(P=matrix(n+1,n+1,r,c,if(r>=c,(r^2)^(r-c)/(r-c)!)), D=matrix(n+1,n+1,r,c,if(r==c,r)));if(n>=k,(P^-1*D^2*P)[n+1,k+1])}

Formula

Matrix diagonalization method: define the triangular matrix P by P(n, k) = ((n+1)^2)^(n-k)/(n-k)! for n >= k >= 0 and the diagonal matrix D by D(n, n) = n+1 for n >= 0; then T is given by T = P^-1*D^2*P.