A107674 Matrix square of triangle A107671.

1, 24, 4, 2268, 135, 9, 461056, 15936, 448, 16, 160977375, 3789250, 69000, 1125, 25, 85624508376, 1485395280, 19994688, 223560, 2376, 36, 64363893844726, 862907827866, 9138674195, 79086196, 596820, 4459, 49, 64928246784463872

Offset: 0

Author

Paul D. Hanna, Jun 07 2005

Keywords

• nonn
• tabl

Comments

Column 0 is A107675.

Examples

			Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
            1;
           24,          4;
         2268,        135,        9;
       461056,      15936,      448,     16;
    160977375,    3789250,    69000,   1125,   25;
  85624508376, 1485395280, 19994688, 223560, 2376, 36;
  ...
		

Crossrefs

Cf. A006690, A107667, A107671, A107675, A107676.

Programs

PARI

{T(n,k)=local(P=matrix(n+1,n+1,r,c,if(r>=c,(r^3)^(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)^3)^(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.