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A005326
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Permanent of `coprime?' matrix.
(Formerly M2382)
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4
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1, 1, 3, 4, 28, 16, 256, 324, 3600, 3600, 129744, 63504, 3521232, 3459600, 60891840, 91240704, 8048712960, 3554067456, 425476094976, 320265446400, 12474417291264, 16417666704384, 2778580249611264, 1142807773593600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Number of perumutations p of (1,2,3,...,n) such that k and p(k) are relatively prime for all k in (1,2,3,...,n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 23 2002
Coprime matrix M=[m(i,j)] is a square matrix defined by m(i,j)=1 if gcd(i,j)=1 else 0.
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REFERENCES
| D. M. Jackson, The combinatorial interpretation of the Jacobi identity from Lie algebra, J. Combin. Theory, A 23 (1977), 233-256.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(2n)=A009679(n)^2 - T. D. Noe (noe(AT)sspectra.com), Feb 10 2007
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MATHEMATICA
| perm[m_?MatrixQ] := With[{v = Array[x, Length[m]]}, Coefficient[Times @@ (m.v), Times @@ v]]; a[n_] := perm[ Table[ Boole[GCD[i, j] == 1], {i, 1, n}, {j, 1, n}]]; Table[an = a[n]; Print[an]; an, {n, 1, 24}](* From Jean-François Alcover, Nov 15 2011 *)
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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(i, j)==1); print1(permRWNb(a)", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007
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CROSSREFS
| Sequence in context: A094084 A042829 A140896 * A100600 A076001 A032833
Adjacent sequences: A005323 A005324 A005325 * A005327 A005328 A005329
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected by Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 05 2003
More terms from T. D. Noe (noe(AT)sspectra.com), Feb 10 2007
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