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%I #11 Jan 27 2021 10:31:53
%S 1,0,-1,-8,-204,-24768,-17867520,-90077184000,-3632037470208000,
%T -1317998813773824000000,-4782755930355924782284800000,
%U -190912318579437962454242426880000000
%N Determinant of the n-th principal submatrix of A204246.
%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 *)
%o (PARI) A204247(n)=matdet(matrix(n,n,i,j,if(min(i,j)==1,1,if(i==j,(i-1)!)))) \\ _M. F. Hasler_, Jan 13 2012
%Y Cf. A204246, A203227.
%K sign
%O 1,4
%A _Clark Kimberling_, Jan 13 2012
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