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A383773 a(n) = pos(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (1, 2, ... , n), and pos(M(n)) is the positive part of the determinant of M(n); see A380661.

%I A383773 #5 May 21 2025 16:40:47
%S A383773 1,1,36,450,17550,744906,47753440,3909436192,410384120220,
%T A383773 53323552728000,8417606908865220,1586195621597483136,
%U A383773 351735343178101060906,90667504180193792086144,26884188980472806091900000,9086147124746080046118543360,3472279409772212369077001352888
%N A383773 a(n) = pos(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (1, 2, ... , n), and pos(M(n)) is the positive part of the determinant of M(n); see A380661.
%e A383773 The rows of M(4) are (1, 2, 3, 4), (4, 1, 2, 3), (3, 4, 1, 2), (2, 3, 4, 1); determinant(M(4)) = -160; permanent(M(4)) = 1060, so neg(M(4)) = (-160 - 1060)/2 = -610 and pos(M(4)) = (-160 + 1060)/2 = 450.
%t A383773 z = 18;
%t A383773 v[n_] := Table[k + 1, {k, 0, n - 1}];
%t A383773 u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]];
%t A383773 p = Table[Simplify[Permanent[u[n]]], {n, 1, z}]   (* A085719 *)
%t A383773 d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A052182 *)
%t A383773 neg = (d - p)/2   (* A383772 *)
%t A383773 pos = (d + p)/2  (* A383773 *)
%Y A383773 Cf. A052182 (determinant), A085719 (permanent), A380661, A383772, A383774, A383775.
%K A383773 nonn
%O A383773 1,3
%A A383773 _Clark Kimberling_, May 17 2025