A393597 a(n) is the permanent of the n X n matrix whose generic element M[i,j] is equal to C(n, (j-i) mod n).

1, 1, 5, 82, 5529, 1305001, 1246227380, 4371464163984, 63016773178936689, 3402552304257053274586, 763565844226555199268790625, 646167055423310071202629440787777, 2286555305348402925289061763545121627792, 30572734528101754143849564382255256328804437905, 1715114378944460721111177450683240739069441328724776192

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Example

a(3) = 82:
  [1, 3, 3]
  [3, 1, 3]
  [3, 3, 1]

Maple

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
         Matrix(n, shape=Circulant[[binomial(n, i)$i=1..n]]))):
seq(a(n), n=0..14);  # Alois P. Heinz, Mar 30 2026

Mathematica

a[0]:=1; a[n_]:=Permanent[Table[Binomial[n, Mod[j-i, n]], {i, n}, {j, n}]]; Array[a, 15, 0]

Prog

(PARI) a(n) = matpermanent(matrix(n, n, i, j, binomial(n, (j-i) % n))); \\ Michel Marcus, Mar 30 2026

Crossrefs

Cf. A048954 (determinant).

Sequence in context: A274388 A308753 A163011 * A368081 A142162 A082546

Adjacent sequences: A393594 A393595 A393596 * A393598 A393599 A393600

Keyword

nonn

Author

Stefano Spezia, Mar 30 2026

Status

approved