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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.

%I A204246 #14 Aug 09 2015 01:05:12
%S A204246 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 A204246 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 A204246 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 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.
%e A204246 Northwest corner:
%e A204246 1 1 1 1 1
%e A204246 1 1 0 0 0
%e A204246 1 0 2 0 0
%e A204246 1 0 0 6 0
%e A204246 1 0 0 0 14
%p A204246 A204246 := proc(n,m)
%p A204246         if n=1 or m =1 then
%p A204246                 1;
%p A204246         elif n = m then
%p A204246                 (n-1)! ;
%p A204246         else
%p A204246                 0;
%p A204246         end if;
%p A204246 end proc:
%p A204246 seq(seq(A204246(d-m,m),m=1..d-1),d=2..15) ; # _R. J. Mathar_, Jan 21 2012
%t A204246 f[i_, j_] := 0; f[1, j_] := 1;
%t A204246 f[i_, 1] := 1; f[i_, i_] := (i - 1)!;
%t A204246 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204246 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204246 Flatten[Table[f[i, n + 1 - i],
%t A204246   {n, 1, 12}, {i, 1, n}]]      (* A204246 *)
%t A204246 Table[Det[m[n]], {n, 1, 15}]  (* A204247 *)
%t A204246 Permanent[m_] :=
%t A204246   With[{a = Array[x, Length[m]]},
%t A204246    Coefficient[Times @@ (m.a), Times @@ a]];
%t A204246 Table[Permanent[m[n]], {n, 1, 14}]  (* A203227 *)
%Y A204246 Cf. A204247, A203227.
%K A204246 nonn,tabl,easy
%O A204246 1,13
%A A204246 _Clark Kimberling_, Jan 13 2012
%E A204246 Terms corrected by _R. J. Mathar_, Jan 21 2012