A371153 a(n) is the permanent of the 2n+1 X 2n+1 matrix P(2n+1) defined by P[1,j] = 1, P[i,j] = i-1 if i<=j, and P[i,i] = i-n-1 otherwise with 1 <= i,j <= 2n+1.

1, -3, 185, -55307, 49980969, -106782742099, 462446644072153, -3649813053096346875, 48540310969531346254217, -1024268653171975469599364291, 32694499032613728282606987622521, -1518591968826504411972243578217645163, 99392870823564324693001427592486103515625

Offset: 0

Author

Stefano Spezia, Mar 13 2024

Keywords

• sign

Comments

The matrices P(2n) have permanent equal to zero.

Examples

			a(3) = -55307:
   1,  1,  1,  1,  1,  1, 1;
  -6,  1,  1,  1,  1,  1, 1;
  -5, -5,  2,  2,  2,  2, 2;
  -4, -4, -4,  3,  3,  3, 3;
  -3, -3, -3, -3,  4,  4, 4;
  -2, -2, -2, -2, -2,  5, 5;
  -1, -1, -1, -1, -1, -1, 6.
		

Crossrefs

Cf. A000169, A005408, A084849 (trace), A085530 (determinant).

Programs

Mathematica

b[n_]:=Permanent[Table[If[i==1, 1, If[i<=j, i-1, i-n-1]], {i, n}, {j, n}]]; a[n_]:=b[2n+1]; Array[a, 10,0]