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A086759 Permanent of the Cayley addition table of Z_{n}. a(n) is the permanent of the n X n matrix M_(i,j) = ((i+j) mod n) where i and j range from 0 to n-1.

%I A086759 #12 Oct 25 2020 02:38:06
%S A086759 0,1,9,164,5050,227508,14064519,1146668608,119249333028,
%T A086759 15400125776000,2417814003691405,453536611741073664,
%U A086759 100178077459552487070,25735749696251388478720,7608415981499790110521875,2564724413131659780025106432,977834710569917222742633274504
%N A086759 Permanent of the Cayley addition table of Z_{n}. a(n) is the permanent of the n X n matrix M_(i,j) = ((i+j) mod n) where i and j range from 0 to n-1.
%H A086759 Stefano Spezia, <a href="/A086759/b086759.txt">Table of n, a(n) for n = 1..36</a>
%H A086759 Robert Connelly, Maurice Pierre, <a href="https://arxiv.org/abs/1907.03652">Maximally Dense Disc Packings on the Plane</a>, arXiv:1907.03652 [math.MG], 2019.
%e A086759 a(9) is the permanent of the matrix
%e A086759 0 1 2 3 4 5 6 7 8
%e A086759 1 2 3 4 5 6 7 8 0
%e A086759 2 3 4 5 6 7 8 0 1
%e A086759 3 4 5 6 7 8 0 1 2
%e A086759 4 5 6 7 8 0 1 2 3
%e A086759 5 6 7 8 0 1 2 3 4
%e A086759 6 7 8 0 1 2 3 4 5
%e A086759 7 8 0 1 2 3 4 5 6
%e A086759 8 0 1 2 3 4 5 6 7
%t A086759 Array[With[{s = Range[0, #]}, Permanent@ Array[RotateLeft[s, #] &, Last@ s + 1, 0]] &, 16, 0] (* _Michael De Vlieger_, Sep 03 2019 *)
%o A086759 (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=1,21,a=matrix(n,n,i,j,((i+j-2)%n));print1(permRWNb(a)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
%o A086759 (PARI) a(n) = matpermanent(matrix(n, n, i, j, (i+j-2) % n)) \\ _Stefano Spezia_, Oct 25 2020
%Y A086759 Cf. A070896, A085719.
%K A086759 nonn
%O A086759 1,3
%A A086759 Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 01 2003
%E A086759 a(9) from Neven Juric (neven.juric(AT)apis-it.hr), Jul 11 2005
%E A086759 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
%E A086759 a(17) from _Michael De Vlieger_, Sep 03 2019