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A204245 Determinant of the n-th principal submatrix of A204244.

%I A204245 #6 Jul 12 2012 00:39:59
%S A204245 1,1,4,84,9792,7015680,35334144000,1424547274752000,
%T A204245 516934658477260800000,1875850653748811739955200000,
%U A204245 74877948716953984356707205120000000,35866656974348638336845775173058560000000000
%N A204245 Determinant of the n-th principal submatrix of A204244.
%t A204245 f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := i!;
%t A204245 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204245 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204245 Flatten[Table[f[i, n + 1 - i],
%t A204245   {n, 1, 12}, {i, 1, n}]]      (* A204244 *)
%t A204245 Table[Det[m[n]], {n, 1, 15}]   (* A204245 *)
%t A204245 Permanent[m_] :=
%t A204245   With[{a = Array[x, Length[m]]},
%t A204245    Coefficient[Times @@ (m.a), Times @@ a]];
%t A204245 Table[Permanent[m[n]], {n, 1, 14}]   (*  A203228 *)
%Y A204245 Cf. A204244, A203228.
%K A204245 nonn
%O A204245 1,3
%A A204245 _Clark Kimberling_, Jan 13 2012