A204245 -id:A204245 - cp's OEIS frontend

A204446 Permanent of the n-th principal submatrix of A204445.

1, 1, 3, 9, 34, 116, 792, 4752, 32304, 202320, 1991952, 17927568, 175473216, 1613364480, 20695108608, 248341303296, 3173837230080, 38575603814400, 610011772416000, 9150176586240000, 144343174487040000, 2183607168215040000

Offset: 1

Clark Kimberling, Jan 15 2012

nonn

Cf. A204245, A204435.

f[i_, j_] :=
Floor[(i + j + 4)/4] - Floor[(i + j + 1)/4];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 14}, {i, 1, n}]]    (* A204445 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}] (* A204446 *)

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

Original entry on oeis.org

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, 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, 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

Offset: 1

Clark Kimberling, Jan 13 2012

			Northwest corner:
1 1 1 1
1 2 0 0
1 0 6 0
1 0 0 24

Cf. A204245, A203228.

f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := i!;
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]      (* A204244 *)
Table[Det[m[n]], {n, 1, 15}]   (* A204245 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}]   (*  A203228 *)

cp's OEIS Frontend

A204446 Permanent of the n-th principal submatrix of A204445.

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