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A130641
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The first entry of the vector v[n]=M[n]v[n-1], where M[n] is a 7 X 7 matrix M[n] = [[n, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0]] and v[0] is the column vector [0, 0, 0, 0, 0, 0, 1].
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%I #4 Mar 30 2012 17:34:21
%S 0,1,2,6,24,120,720,5040,40321,362891,3628916,39918100,479017320,
%T 6227225880,87181167360,1307717550721,20923481174427,355699183594175,
%U 6402585344613250,121649122026669070,2432982446760607280
%N The first entry of the vector v[n]=M[n]v[n-1], where M[n] is a 7 X 7 matrix M[n] = [[n, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0]] and v[0] is the column vector [0, 0, 0, 0, 0, 0, 1].
%t M[n_] := {{n,0,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0},{0,0,1,0,0,0,0},{0,0,0,1,0,0,0},{0, 0,0,0,1,0,0},{0,0,0,0,0,1,0}}; v[0] = {0,0,0,0,0,0,1}; v[n_] := M[n].v[n - 1]; Table[v[n][[1]], {n, 0, 30}]
%K nonn
%O 0,3
%A _Roger L. Bagula_, Jun 19 2007
%E Edited by _N. J. A. Sloane_, Jul 23 2007
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