A204246 Array given by f(i,1)=1, f(1,j)=1, f(i,i)=(i-1)!, and f(i,j)=0 otherwise, read by antidiagonals.

1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 6, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 24, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 120, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Clark Kimberling, Jan 13 2012

Keywords

• nonn
• tabl
• easy

Examples

			Northwest corner:
1 1 1 1 1
1 1 0 0 0
1 0 2 0 0
1 0 0 6 0
1 0 0 0 14
		

Crossrefs

Cf. A204247, A203227.

Programs

Maple

A204246 := proc(n,m)
        if n=1 or m =1 then
                1;
        elif n = m then
                (n-1)! ;
        else
                0;
        end if;
end proc:
seq(seq(A204246(d-m,m),m=1..d-1),d=2..15) ; # R. J. Mathar, Jan 21 2012

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 *)

Extensions

Terms corrected by R. J. Mathar, Jan 21 2012