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A009679 Number of partitions of {1, ..., 2n} into coprime pairs. 2


%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,2j-1) 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^(n-1)-1,sg=-sg;j=valuation(k,2)+1;z=1-2*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*j-1)==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

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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)