A330287 Permanent of the n-th principal submatrix M(n) of A319840.

1, 1, 8, 208, 11488, 1093056, 158972160, 32734095360, 9049229328384, 3230305304002560, 1445344680438005760, 791762592707031859200, 521023492500173338705920, 405448567547957922512240640, 368210800911998093644372377600, 385879616532879866123928993792000, 462151848929747968377341029122048000

Offset: 0

Author

Stefano Spezia, Dec 11 2019

Keywords

• nonn

Comments

The matrix M(n) is defined as M[i,j,n] = i*j if i < 3 or j < 3 and M[i,j,n] = 2*(i + j) - 4 otherwise.

det(M(0)) = det(M(1)) = 1 and det(M(n)) = 0 for n > 1.

For n > 0, the trace of the matrix M(n) is A001844(n-1).

For n > 0, the antitrace of the matrix M(n) is A005893(n-1).

For n > 1, the super- and subdiagonal sum is A001105(n-1).

Examples

			For n = 1 the matrix M(1) is
  1
with permanent a(1) = 1.
For n = 2 the matrix M(2) is
  1, 2
  2, 4
with permanent a(2) = 8.
For n = 3 the matrix M(3) is
  1,  2,  3
  2,  4,  6
  3,  6,  8
with permanent a(3) = 208.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..35

Crossrefs

Cf. A001105, A001844, A005893, A319840.

Programs

PARI

tm(n) = matrix(n, n, i, j, if ((i<3) || (j<3), i*j, 2*(i+j)-4));
a(n) = matpermanent(tm(n));

Formula

a(n) ~ c * A238261^n * n!^2 / sqrt(n), where c = 0.0286685259829... - Vaclav Kotesovec, Aug 19 2021