A390821 a(n) is the permanent of the unipotent Sylvester-Kac tridiagonal matrix of order n having main diagonal [0, 2, ..., 2*(n-1)], superdiagonal [1, 2, ..., n-1], and [subdiagonal 1-n, 2-n, ..., -1].

1, 0, -1, -8, -63, -512, -4025, -24192, 71393, 7340032, 212453199, 4904704000, 99297793441, 1698013642752, 18399513215447, -262521103351808, -27936205104189375, -1306063683146743808, -48317430820180084577, -1516823363388524986368, -38246308373621093669119

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Zhibin Du and Carlos M. da Fonseca, On an infinite family of unipotent Sylvester-Kac-like matrices, Notes on Number Theory and Discrete Mathematics, Volume 31, 2025, Number 4, Pages 846-850. See section 2.

Example

a(4) = -63:
  [ 0,  1,  0, 0]
  [-3,  2,  2, 0]
  [ 0, -2,  4, 3]
  [ 0,  0, -1, 6]

Mathematica

M[i_, j_, n_]:=If[j==i+1, i, If[i==j+1, -(n-i+1), If[i==j, 2(i-1), 0]]]; a[n_]:=Permanent[Table[M[i, j, n], {i, n}, {j, n}]]; Array[a, 18]

Crossrefs

Cf. A065440 (determinant).

Sequence in context: A001090 A395831 A387841 * A243782 A369810 A105219

Adjacent sequences: A390818 A390819 A390820 * A390822 A390823 A390824

Keyword

sign

Author

Stefano Spezia, Nov 20 2025

Status

approved