A204245 Determinant of the n-th principal submatrix of A204244.

1, 1, 4, 84, 9792, 7015680, 35334144000, 1424547274752000, 516934658477260800000, 1875850653748811739955200000, 74877948716953984356707205120000000, 35866656974348638336845775173058560000000000

Offset: 1

Author

Clark Kimberling, Jan 13 2012

Keywords

• nonn

Crossrefs

Cf. A204244, A203228.

Programs

Mathematica

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 *)