|
| |
|
|
A107056
|
|
Matrix inverse of A103247, so that T(n,k) = C(n,k)*A010842(n-k), read by rows.
|
|
0
| |
|
|
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
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
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.
|
|
|
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 * A116384 A117207 A046658
Adjacent sequences: A107053 A107054 A107055 * A107057 A107058 A107059
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 19 2005
|
| |
|
|
