A085719 Permanent of n X n matrix whose rows are cyclic permutations of 1..n.

1, 1, 5, 54, 1060, 33225, 1517028, 95036284, 7828309568, 820553006835, 106652605456000, 16835058193182834, 3172396072749375744, 703470523269606264445, 181335014313248383578368, 53768377727402203980675000, 18172294259291992881395286016

Offset: 0

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 19 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..23 (terms n=1..22 from Herman Jamke)
• Wikipedia, Permanent (mathematics)

Crossrefs

Cf. A052182, A070896.

Programs

Maple

a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
         Matrix(n, (i, j)-> 1+irem(j+i, n)))):
seq(a(n), n=0..17);  # Alois P. Heinz, Apr 28 2020

PARI

permRWNb(a)=n=matsize(a)[1];if(n==1,return(a[1,1]));sg=1;in=vectorv(n);x=in;x=a[,n]-sum(j=1,n,a[,j])/2;p=prod(i=1,n,x[i]);for(k=1,2^(n-1)-1,sg=-sg;j=valuation(k,2)+1;z=1-2*in[j];in[j]+=z;x+=z*a[,j];p+=prod(i=1,n,x[i],sg));return(2*(2*(n%2)-1)*p)
for(n=1,22,a=matrix(n,n,i,j,1+(j-i)%n);print1(permRWNb(a)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007

Sage

def A085719(n) : return matrix([[(i-j)%n+1 for j in range(n)] for i in range(n)]).permanent() # Eric M. Schmidt, May 04 2013

Extensions

More terms from Vladeta Jovovic, Jul 21 2003

a(0)=1 prepended by Alois P. Heinz, Apr 28 2020