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 A085807 Permanent of the symmetric n X n matrix A defined by A[i,j] = |i-j| for 1 <= i,j <= n. 7

%I

%S 1,0,1,4,64,1152,34372,1335008,69599744,4577345152,374491314176,

%T 37154032517376,4402467119882240,613680867638476800,

%U 99443966100565999872,18534733913629064343552,3937496200758879526977536,945776134421421651222708224,255043190756805184245158084608

%N Permanent of the symmetric n X n matrix A defined by A[i,j] = |i-j| for 1 <= i,j <= n.

%H Vaclav Kotesovec, <a href="/A085807/b085807.txt">Table of n, a(n) for n = 0..32</a>

%p with(LinearAlgebra):

%p a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> abs(i-j)))):

%p seq(a(n), n=0..18); # _Alois P. Heinz_, Nov 14 2016

%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) for(n=1,22,a=matrix(n,n,i,j,abs(i-j));print1(permRWNb(a)",")) - Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007

%Y Cf. A085750, A204249, A278845, A278847.

%K nonn

%O 0,4

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 24 2003

%E More terms from _Vladeta Jovovic_, Jul 26 2003

%E a(0)=1 prepended by _Alois P. Heinz_, Nov 14 2016

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Last modified April 20 02:06 EDT 2019. Contains 322291 sequences. (Running on oeis4.)