0,2

A103247(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n by n matrix with 3's on the diagonal and 1's elsewhere.

T(n, k) = n!/k!*Sum_{j=0..n-k} 2^(n-k-j)/(n-k-j)!.

Triangle T begins:

1;

3,1;

10,6,1;

38,30,9,1;

168,152,60,12,1;

872,840,380,100,15,1;

5296,5232,2520,760,150,18,1; ...

where T(n,k) = A010842(n-k)*binomial(n,k).

Matrix logarithm L begins:

0;

-3,0;

-1,-6,0;

-2,-3,-9,0;

-6,-8,-6,-12,0;

-24,-30,-20,-10,-15,0; ...

where L(n,k) = L(n,0)*binomial(n,k),

with L(n,0)=-(n-1)! for n>1, L(1,0)=-3, L(0,0)=0.

(PARI) T(n, k)=n!/k!*sum(j=0, n-k, 2^(n-k-j)/(n-k-j)!)

Cf. A103247, A010842.

Sequence in context: A134283 A035324 A091965 this_sequence A116384 A117207 A046658

Adjacent sequences: A107053 A107054 A107055 this_sequence A107057 A107058 A107059

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), May 19 2005