cp's OEIS Frontend

A110504 Triangle, read by rows, which equals the matrix logarithm of the triangle A110503.

%I A110504 #6 Jun 13 2017 22:21:56
%S A110504 0,1,0,3,-1,0,7,-3,1,0,30,-7,3,-1,0,144,-30,7,-3,1,0,876,-144,30,-7,3,
%T A110504 -1,0,6084,-876,144,-30,7,-3,1,0,48816,-6084,876,-144,30,-7,3,-1,0,
%U A110504 438624,-48816,6084,-876,144,-30,7,-3,1,0,4389120,-438624,48816,-6084,876,-144,30,-7,3,-1,0
%N A110504 Triangle, read by rows, which equals the matrix logarithm of the triangle A110503.
%C A110504 The unsigned columns this triangle are all equal to A110505. Triangle A110503 shifts one column left under matrix inverse.
%F A110504 T(n, k) = (-1)^k*A110505(n-k).
%e A110504 Triangle begins:
%e A110504 0;
%e A110504 1/1!, 0;
%e A110504 3/2!, -1/1!, 0;
%e A110504 7/3!, -3/2!, 1/1!, 0;
%e A110504 30/4!, -7/3!, 3/2!, -1/1!, 0;
%e A110504 144/5!, -30/4!, 7/3!, -3/2!, 1/1!, 0;
%e A110504 876/6!, -144/5!, 30/4!, -7/3!, 3/2!, -1/1!, 0;
%e A110504 6084/7!, -876/6!, 144/5!, -30/4!, 7/3!, -3/2!, 1/1!, 0; ...
%e A110504 Unsigned columns all equal A110505.
%e A110504 Exponential function of matrix equals A110503:
%e A110504 1;
%e A110504 1,1;
%e A110504 1,-1,1;
%e A110504 1,-2,1,1;
%e A110504 1,-1,1,-1,1;
%e A110504 1,-1,1,-2,1,1;
%e A110504 1,-1,1,-1,1,-1,1;
%e A110504 1,-1,1,-1,1,-2,1,1; ...
%o A110504 (PARI) T(n,k)=local(M=matrix(n+1,n+1,r,c,if(r>=c, if(r==c || c%2==1,1,if(r%2==0 && r==c+2,-2,-1))))); sum(i=1,#M,-(M^0-M)^i/i)[n+1,k+1]
%Y A110504 Cf. A110503 (matrix exponential), A110505 (unsigned columns).
%K A110504 sign,tabl
%O A110504 0,4
%A A110504 _Paul D. Hanna_, Jul 23 2005