Search: id:A101811
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%I A101811
%S A101811 1,7,647,32547,32104903,5850859031888599,29453515169174062608487,
%T A101811 2335404534493957255219087217249,
%U A101811 418207321191051873285940121750107840759
%N A101811 Numerator of the permanent of the n-th Hilbert matrix.
%H A101811 Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007, <a href="b101811.txt">
               Table of n, a(n) for n = 1..21</a>
%F A101811 Numer(permanent(matrix(1/(i+j-1);i, j=1, ..., n)))
%e A101811 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 A101811 with(linalg): seq(numer(permanent(hilbert(n))),n=1..12);
%o A101811 (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 A101811 Cf. A101812.
%Y A101811 Sequence in context: A109542 A052132 A052134 this_sequence A092326 A074282 
               A013568
%Y A101811 Adjacent sequences: A101808 A101809 A101810 this_sequence A101812 A101813 
               A101814
%K A101811 nonn,frac
%O A101811 1,2
%A A101811 Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 16 2004

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