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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 19 11:11 EDT 2019. Contains 324219 sequences. (Running on oeis4.)