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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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1
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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, 117649, 117649, 16807, 49, 9, 81, 117369, 59049, 33480783, 930196594089, 4238886345135097131, 169560200598623521407
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OFFSET
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1,4
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LINKS
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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}] (* Robert G. Wilson v, Feb 06 2004 *)
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PROG
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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
(PARI) for(n=1, 25, a=mathilbert(n); print1(1 / (matdet(a) * denominator(matpermanent(a)))", ")) \\ Vaclav Kotesovec, Aug 13 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(22) and a(23) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 10 2007
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STATUS
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approved
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