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.

1, 1, 36, 450, 17550, 744906, 47753440, 3909436192, 410384120220, 53323552728000, 8417606908865220, 1586195621597483136, 351735343178101060906, 90667504180193792086144, 26884188980472806091900000, 9086147124746080046118543360, 3472279409772212369077001352888

Offset: 1

Author

Clark Kimberling, May 17 2025

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A052182 (determinant), A085719 (permanent), A380661, A383772, A383774, A383775.

Programs

Mathematica

z = 18;
v[n_] := Table[k + 1, {k, 0, n - 1}];
u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]];
p = Table[Simplify[Permanent[u[n]]], {n, 1, z}]   (* A085719 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A052182 *)
neg = (d - p)/2   (* A383772 *)
pos = (d + p)/2  (* A383773 *)