A204244 - OEIS

%I #6 Mar 30 2012 18:58:08

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

%e Northwest corner:

%e 1 1 1 1

%e 1 2 0 0

%e 1 0 6 0

%e 1 0 0 24

%t f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := i!;

%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

%t TableForm[m[8]] (* 8x8 principal submatrix *)

%t Flatten[Table[f[i, n + 1 - i],

%t   {n, 1, 12}, {i, 1, n}]]      (* A204244 *)

%t Table[Det[m[n]], {n, 1, 15}]   (* A204245 *)

%t Permanent[m_] :=

%t   With[{a = Array[x, Length[m]]},

%t    Coefficient[Times @@ (m.a), Times @@ a]];

%t Table[Permanent[m[n]], {n, 1, 14}]   (*  A203228 *)

%Y Cf. A204245, A203228.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_, Jan 13 2012