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%I #24 Apr 28 2020 18:56:44
%S 1,1,5,54,1060,33225,1517028,95036284,7828309568,820553006835,
%T 106652605456000,16835058193182834,3172396072749375744,
%U 703470523269606264445,181335014313248383578368,53768377727402203980675000,18172294259291992881395286016
%N Permanent of n X n matrix whose rows are cyclic permutations of 1..n.
%H Alois P. Heinz, <a href="/A085719/b085719.txt">Table of n, a(n) for n = 0..23</a> (terms n=1..22 from Herman Jamke)
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permanent_(mathematics)">Permanent (mathematics)</a>
%p a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](
%p Matrix(n, (i, j)-> 1+irem(j+i, n)))):
%p seq(a(n), n=0..17); # _Alois P. Heinz_, Apr 28 2020
%o (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)
%o 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
%o (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
%Y Cf. A052182, A070896.
%K nonn
%O 0,3
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 19 2003
%E More terms from _Vladeta Jovovic_, Jul 21 2003
%E a(0)=1 prepended by _Alois P. Heinz_, Apr 28 2020
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