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

0,2

Comments

Column 0 is A107675.

Links

Table of n, a(n) for n=0..28.

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.

Example

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;
  ...

Prog

(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])}

Crossrefs

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

Sequence in context: A267285 A040563 A184763 * A040560 A040558 A215752

Adjacent sequences: A107671 A107672 A107673 * A107675 A107676 A107677

Keyword

nonn,tabl

Author

Paul D. Hanna, Jun 07 2005

Status

approved