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%I #12 Jan 07 2016 03:48:17
%S 1,7,647,32547,32104903,5850859031888599,29453515169174062608487,
%T 2335404534493957255219087217249,
%U 418207321191051873285940121750107840759
%N Numerator of the permanent of the n-th Hilbert matrix.
%H Charles R Greathouse IV, <a href="/A101811/b101811.txt">Table of n, a(n) for n = 1..25</a>
%F Numer(permanent(matrix(1/(i+j-1);i, j=1, ..., n)))
%e a(2)=7 because the Hilbert matrix is [[1,1/2],[1/2,1/3]] and its permanent is 1*1/3 + (1/2)*(1/2)=7/12.
%p with(linalg): seq(numer(permanent(hilbert(n))),n=1..12);
%t hilbert[n_] := Table[1/(i + j - 1), {i, 1, n}, {j, 1, n}]; a[n_] := Permanent[hilbert[n]] // Numerator; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 9}] (* _Jean-François Alcover_, Jan 07 2016 *)
%o (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) num=[];den=[];for(n=1,20,a=matrix(n,n,i,j,1/(i+j-1));p=permRWNb(a);num=concat(num,numerator(p));den=concat(den,denominator(p)));num - Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007
%Y Cf. A101812.
%K nonn,frac
%O 1,2
%A _Emeric Deutsch_, Dec 16 2004
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