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

1,13

Links

Table of n, a(n) for n=1..103.

Example

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

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 *)

Crossrefs

Cf. A204247, A203227.

Sequence in context: A158924 A025426 A269244 * A053200 A050870 A103306

Adjacent sequences: A204243 A204244 A204245 * A204247 A204248 A204249

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Jan 13 2012

Extensions

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

Status

approved