A107056 Matrix inverse of A103247, so that T(n,k) = C(n,k)*A010842(n-k), read by rows.

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, 37200, 37072, 18312, 5880, 1330, 210, 21, 1, 297856, 297600, 148288, 48832, 11760, 2128, 280, 24, 1, 2681216, 2680704, 1339200, 444864, 109872

Offset: 0

Author

Paul D. Hanna, May 19 2005

Keywords

• nonn
• tabl

Comments

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

Examples

			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.
		

Crossrefs

Cf. A103247, A010842.

Programs

PARI

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

Formula

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