A204247 Determinant of the n-th principal submatrix of A204246.

1, 0, -1, -8, -204, -24768, -17867520, -90077184000, -3632037470208000, -1317998813773824000000, -4782755930355924782284800000, -190912318579437962454242426880000000

Offset: 1

Author

Clark Kimberling, Jan 13 2012

Keywords

• sign

Crossrefs

Cf. A204246, A203227.

Programs

Mathematica

f[i_, j_] := 0; f[1, j_] := 1;
f[i_, 1] := 1; f[i_, i_] := (i - 1)!;
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}]]     (* A204246 *)
Table[Det[m[n]], {n, 1, 15}]  (* A204247 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}]  (* A203227 *)

PARI

A204247(n)=matdet(matrix(n,n,i,j,if(min(i,j)==1,1,if(i==j,(i-1)!)))) \\ M. F. Hasler, Jan 13 2012