%I A109516
%S A109516 1,1,6,45,464,6000,93528,1707111,35721216,843160671,22165100000,
%T A109516 642268811184,20339749638144,698946255836933,25903663544572800,
%U A109516 1029945249481640625,43733528272753917952,1975222567881226040760
%N A109516 a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;n-1,n-1].
%C A109516 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 A109516 a(4)=45 because if M is the 2 X 2 matrix [0,1;3,3], then M^4 is the 2 
               X 2 matrix [36,45;135;171].
%p A109516 with(linalg): a:=proc(n) local A,k: A[1]:=matrix(2,2,[0,1,n-1,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..20);
%t A109516 M[n_] = If[n > 1, MatrixPower[{{0, 1}, {n - 1, n - 1}}, n], {{0, 1}, 
               {1, 1}}] a = Table[M[n][[1, 2]], {n, 1, 50}]
%Y A109516 Cf. A000045, A000166.
%Y A109516 Sequence in context: A019577 A097814 A084064 this_sequence A078865 A160492 
               A086721
%Y A109516 Adjacent sequences: A109513 A109514 A109515 this_sequence A109517 A109518 
               A109519
%K A109516 nonn
%O A109516 1,3
%A A109516 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 16 2005