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Search: id:A061914
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| A061914 |
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Let H_n = n-th Hilbert matrix; sequence gives 1 / ( det(H_n) * denominator(permanent(H_n)) ). |
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2
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| 1, 1, 1, 27, 567, 1, 1, 1, 7, 9, 5103, 1275989841, 992436543, 48629390607, 169706648853, 40257567, 63, 1, 7, 31, 1, 3969, 25865973
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = 1/(denominator(permanent(hilbert(n)))*det(hilbert(n))), where hilbert(n) denotes the n-th Hilbert matrix.
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MAPLE
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with(linalg): seq(1/(denom(permanent(hilbert(n)))*det(hilbert(n))), n=1..16);
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MATHEMATICA
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Permanent[m_List] := With[{v = Array[x, Length[m]]}, Coefficient[Times @@ (m.v), Times @@ v]]; f[n_] := Block[{i = Table[1/(i + j - 1), {i, n}, {j, n}]}, 1/(Det[i]Denominator[Permanent[i]])]; Table[ f[n], {n, 1, 18}] (from Robert G. Wilson v Feb 06 2004)
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PROGRAM
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(PARI) permRWN(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); n1=n-1; sg=1; m=1; nc=0; in=vector(n); x=in; for(i=1, n, x[i]=a[i, n]-sum(j=1, n, a[i, j])/2); p=prod(i=1, n, x[i]); while(m, sg=-sg; j=1; if((nc%2)!=0, j++; while(in[j-1]==0, j++)); in[j]=1-in[j]; nc+=2*in[j]-1; m=nc!=in[n1]; z=2*in[j]-1; for(i=1, n, x[i]+=z*a[i, j]); p+=sg*prod(i=1, n, x[i])); return(2*(2*(n%2)-1)*p) for(n=1, 23, a=mathilbert(n); print1(1/(matdet(a)*denominator(permRWN(a)))", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), May 10 2007
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CROSSREFS
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Cf. A005249.
Sequence in context: A163199 A051561 A163197 this_sequence A076008 A099753 A046359
Adjacent sequences: A061911 A061912 A061913 this_sequence A061915 A061916 A061917
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KEYWORD
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nonn,more
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AUTHOR
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Asher Auel (asher.auel(AT)reed.edu), May 20 2001
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EXTENSIONS
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a(18)-a(20) from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 09 2004
a(21) from Eric Weisstein (eric(AT)weisstein.com), Feb 19, 2004
a(22) and a(23) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 10 2007
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