%I
%S 1,2,4,18,60,252,1860,9552,59616,565920,4051872,33805440,465239808,
%T 4294865664,35413136640,768372168960,8757710173440,79772814777600,
%U 1986906367584000,22082635812268800,280886415019776000,7683780010315046400
%N Number of partitions of {1, ..., 2n} into coprime pairs.
%F a(n) = sqrt(A005326(2n))  _T. D. Noe_, Feb 10 2007
%F a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether gcd(2i,2j1) is 1 or >1, respectively.  _T. D. Noe_, Feb 11 2007
%o (PARI) permRWNb(a)=n=matsize(a)[1];if(n==1,return(a[1,1]));sg=1;nc=0;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^(n1)1,sg=sg;j=valuation(k,2)+1;z=12*in[j];in[j]+=z;nc+=z;x+=z*a[,j];p+=prod(i=1,n,x[i],sg));return(2*(2*(n%2)1)*p) for(n=1,26,a=matrix(n,n,i,j,gcd(2*i,2*j1)==1);print1(permRWNb(a)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007
%Y Cf. A001147 for the number of partitions (pairings) in unrestricted pairs.
%K nonn
%O 1,2
%A _David W. Wilson_
%E More terms from _T. D. Noe_, Feb 10 2007
%E More terms from _T. D. Noe_, Feb 11 2007
