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

0,2

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.

Links

Table of n, a(n) for n=0..49.

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A103247, A010842.

Sequence in context: A171814 A091965 A171568 * A365962 A337273 A116384

Adjacent sequences: A107053 A107054 A107055 * A107057 A107058 A107059

Keyword

nonn,tabl

Author

Paul D. Hanna, May 19 2005

Status

approved