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

0,3

Links

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

Wikipedia, Permanent (mathematics)

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

Prog

(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

Crossrefs

Cf. A052182, A070896.

Sequence in context: A359617 A223896 A245765 * A129420 A247711 A284066

Adjacent sequences: A085716 A085717 A085718 * A085720 A085721 A085722

Keyword

nonn

Author

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

Extensions

More terms from Vladeta Jovovic, Jul 21 2003

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

Status

approved