cp's OEIS Frontend

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

%I A107056 #6 Mar 30 2012 18:36:46
%S A107056 1,3,1,10,6,1,38,30,9,1,168,152,60,12,1,872,840,380,100,15,1,5296,
%T A107056 5232,2520,760,150,18,1,37200,37072,18312,5880,1330,210,21,1,297856,
%U A107056 297600,148288,48832,11760,2128,280,24,1,2681216,2680704,1339200,444864,109872
%N A107056 Matrix inverse of A103247, so that T(n,k) = C(n,k)*A010842(n-k), read by rows.
%C A107056 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.
%F A107056 T(n, k) = n!/k!*Sum_{j=0..n-k} 2^(n-k-j)/(n-k-j)!.
%e A107056 Triangle T begins:
%e A107056 1;
%e A107056 3,1;
%e A107056 10,6,1;
%e A107056 38,30,9,1;
%e A107056 168,152,60,12,1;
%e A107056 872,840,380,100,15,1;
%e A107056 5296,5232,2520,760,150,18,1; ...
%e A107056 where T(n,k) = A010842(n-k)*binomial(n,k).
%e A107056 Matrix logarithm L begins:
%e A107056 0;
%e A107056 -3,0;
%e A107056 -1,-6,0;
%e A107056 -2,-3,-9,0;
%e A107056 -6,-8,-6,-12,0;
%e A107056 -24,-30,-20,-10,-15,0; ...
%e A107056 where L(n,k) = L(n,0)*binomial(n,k),
%e A107056 with L(n,0)=-(n-1)! for n>1, L(1,0)=-3, L(0,0)=0.
%o A107056 (PARI) T(n,k)=n!/k!*sum(j=0,n-k,2^(n-k-j)/(n-k-j)!)
%Y A107056 Cf. A103247, A010842.
%K A107056 nonn,tabl
%O A107056 0,2
%A A107056 _Paul D. Hanna_, May 19 2005