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%I #2 Mar 30 2012 17:34:19
%S -1,-2,-14,-180,-3344,-80750,-2394792,-84150248,-3417051136,
%T -157409163162,-8109659900000,-462005414448732,-28837128777928704,
%U -1956971256267512966,-143459789419986793600,-11297467798871681250000,-951158499840260908777472
%N a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,2*(n-1)].
%C The (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;1,1] is the Fibonacci number A000045(n).
%e a(4)=-180 because if M is the 2 X 2 matrix [0,-1;3,6], then M^4 is the 2 X 2 matrix [ -99,-180,540,981].
%p with(linalg): a:=proc(n) local A,k: A[1]:=matrix(2,2,[0,-1,n-1,2*(n-1)]): for k from 2 to n do A[k]:=multiply(A[k-1],A[1]) od: A[n][1,2] end: seq(a(n),n=1..19);
%t M[n_] = If[n > 1, MatrixPower[{{0, -1}, {n - 1, 2*(n - 1)}}, n], {{0, 1}, {1, 1}}] a = Table[Abs[M[n][[1, 2]]], {n, 1, 50}]
%Y Cf. A000045, A000166.
%K sign
%O 1,2
%A _Roger L. Bagula_, Jun 16 2005
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