A204246 - OEIS

%I #14 Aug 09 2015 01:05:12

%S 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,

%T 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,

%U 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

%N 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.

%e Northwest corner:

%e 1 1 1 1 1

%e 1 1 0 0 0

%e 1 0 2 0 0

%e 1 0 0 6 0

%e 1 0 0 0 14

%p A204246 := proc(n,m)

%p         if n=1 or m =1 then

%p                 1;

%p         elif n = m then

%p                 (n-1)! ;

%p         else

%p                 0;

%p         end if;

%p end proc:

%p seq(seq(A204246(d-m,m),m=1..d-1),d=2..15) ; # _R. J. Mathar_, Jan 21 2012

%t f[i_, j_] := 0; f[1, j_] := 1;

%t f[i_, 1] := 1; f[i_, i_] := (i - 1)!;

%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

%t TableForm[m[8]] (* 8x8 principal submatrix *)

%t Flatten[Table[f[i, n + 1 - i],

%t   {n, 1, 12}, {i, 1, n}]]      (* A204246 *)

%t Table[Det[m[n]], {n, 1, 15}]  (* A204247 *)

%t Permanent[m_] :=

%t   With[{a = Array[x, Length[m]]},

%t    Coefficient[Times @@ (m.a), Times @@ a]];

%t Table[Permanent[m[n]], {n, 1, 14}]  (* A203227 *)

%Y Cf. A204247, A203227.

%K nonn,tabl,easy

%O 1,13

%A _Clark Kimberling_, Jan 13 2012

%E Terms corrected by _R. J. Mathar_, Jan 21 2012