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A009679
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Number of partitions of {1, ..., 2n} into coprime pairs.
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1
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1, 2, 4, 18, 60, 252, 1860, 9552, 59616, 565920, 4051872, 33805440, 465239808, 4294865664, 35413136640, 768372168960, 8757710173440, 79772814777600, 1986906367584000, 22082635812268800, 280886415019776000, 7683780010315046400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)=sqrt(A005326(2n)) - T. D. Noe (noe(AT)sspectra.com), Feb 10 2007
a(n)=permanent(m), where the n-by-n matrix m is defined m(i,j) = 1 or 0, depending on whether gcd(2i,2j-1) is 1 or >1, respectively. - T. D. Noe (noe(AT)sspectra.com), Feb 11 2007
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PROG
| (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
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CROSSREFS
| Cf. A001147 for the number of partitions (pairings) in unrestricted pairs.
Sequence in context: A093045 A083694 A179040 * A007727 A052689 A139104
Adjacent sequences: A009676 A009677 A009678 * A009680 A009681 A009682
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| More terms from T. D. Noe (noe(AT)sspectra.com), Feb 10 2007
More terms from T. D. Noe (noe(AT)sspectra.com), Feb 11 2007
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