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A107674 Matrix square of triangle A107671. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 06:10 EDT 2021. Contains 348035 sequences. (Running on oeis4.)