Search: id:A061914
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%I A061914
%S A061914 1,1,1,27,567,1,1,1,7,9,5103,1275989841,992436543,48629390607,
%T A061914 169706648853,40257567,63,1,7,31,1,3969,25865973
%N A061914 Let H_n = n-th Hilbert matrix; sequence gives 1 / ( det(H_n) * denominator(permanent(H_n)) 
               ).
%H A061914 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Permanent.html">Link to a section of The World of Mathematics.</a>
%F A061914 a(n) = 1/(denominator(permanent(hilbert(n)))*det(hilbert(n))), where 
               hilbert(n) denotes the n-th Hilbert matrix.
%p A061914 with(linalg): seq(1/(denom(permanent(hilbert(n)))*det(hilbert(n))), n=1..16);
%t A061914 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)
%o A061914 (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
%Y A061914 Cf. A005249.
%Y A061914 Sequence in context: A163199 A051561 A163197 this_sequence A076008 A099753 
               A046359
%Y A061914 Adjacent sequences: A061911 A061912 A061913 this_sequence A061915 A061916 
               A061917
%K A061914 nonn,more
%O A061914 1,4
%A A061914 Asher Auel (asher.auel(AT)reed.edu), May 20 2001
%E A061914 a(18)-a(20) from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 09 2004
%E A061914 a(21) from Eric Weisstein (eric(AT)weisstein.com), Feb 19, 2004
%E A061914 a(22) and a(23) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 10 
               2007

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