login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A009679 Number of partitions of {1, ..., 2n} into coprime pairs. 2

%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,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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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