1,2

Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007, Table of n, a(n) for n = 1..21

Denom(permanent(matrix(1/(i+j-1);i, j=1, ..., n)))

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.

with(linalg): seq(denom(permanent(hilbert(n))), n=1..12);

(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))); den - Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007

Cf. A101811.

Sequence in context: A004823 A009063 A012675 this_sequence A064074 A005249 A129206

Adjacent sequences: A101809 A101810 A101811 this_sequence A101813 A101814 A101815

nonn,frac

Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 16 2004