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A204244 Symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=i! and f(i,j)=0 otherwise.

%I A204244 #6 Mar 30 2012 18:58:08
%S A204244 1,1,1,1,2,1,1,0,0,1,1,0,6,0,1,1,0,0,0,0,1,1,0,0,24,0,0,1,1,0,0,0,0,0,
%T A204244 0,1,1,0,0,0,120,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,720,0,0,0,0,1,
%U A204244 1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,5040,0,0,0,0,0,1,1,0,0,0
%N A204244 Symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=i! and f(i,j)=0 otherwise.
%e A204244 Northwest corner:
%e A204244 1 1 1 1
%e A204244 1 2 0 0
%e A204244 1 0 6 0
%e A204244 1 0 0 24
%t A204244 f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := i!;
%t A204244 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204244 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204244 Flatten[Table[f[i, n + 1 - i],
%t A204244   {n, 1, 12}, {i, 1, n}]]      (* A204244 *)
%t A204244 Table[Det[m[n]], {n, 1, 15}]   (* A204245 *)
%t A204244 Permanent[m_] :=
%t A204244   With[{a = Array[x, Length[m]]},
%t A204244    Coefficient[Times @@ (m.a), Times @@ a]];
%t A204244 Table[Permanent[m[n]], {n, 1, 14}]   (*  A203228 *)
%Y A204244 Cf. A204245, A203228.
%K A204244 nonn,tabl
%O A204244 1,5
%A A204244 _Clark Kimberling_, Jan 13 2012