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A085719 Permanent of n X n matrix whose rows are cyclic permutations of 1..n. 2
1, 1, 5, 54, 1060, 33225, 1517028, 95036284, 7828309568, 820553006835, 106652605456000, 16835058193182834, 3172396072749375744, 703470523269606264445, 181335014313248383578368, 53768377727402203980675000, 18172294259291992881395286016 (list; graph; refs; listen; history; text; internal format)
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: A251583 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

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Last modified September 27 15:44 EDT 2021. Contains 347691 sequences. (Running on oeis4.)