A009679 - OEIS

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A009679

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

1, 2, 4, 18, 60, 252, 1860, 9552, 59616, 565920, 4051872, 33805440, 465239808, 4294865664, 35413136640, 768372168960, 8757710173440, 79772814777600, 1986906367584000, 22082635812268800, 280886415019776000, 7683780010315046400

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OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..30 calculated by Herman Jamke's code.

Carl Pomerance, Coprime permutations, arXiv:2203.03085 [math.NT], 2022.

FORMULA

a(n) = sqrt(A005326(2n)). - T. D. Noe, Feb 10 2007

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

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

CROSSREFS

Cf. A001147 for the number of partitions (pairings) in unrestricted pairs.

Sequence in context: A083694 A179040 A241685 * A007727 A303352 A226011

Adjacent sequences: A009676 A009677 A009678 * A009680 A009681 A009682

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

More terms from T. D. Noe, Feb 10 2007

More terms from T. D. Noe, Feb 11 2007

STATUS

approved