A101811 Numerator of the permanent of the n-th Hilbert matrix.

1, 7, 647, 32547, 32104903, 5850859031888599, 29453515169174062608487, 2335404534493957255219087217249, 418207321191051873285940121750107840759

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..25

Formula

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

Example

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.

Maple

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A101812.

Sequence in context: A109542 A052132 A052134 * A092326 A344049 A347507

Adjacent sequences: A101808 A101809 A101810 * A101812 A101813 A101814

Keyword

nonn,frac

Author

Emeric Deutsch, Dec 16 2004

Status

approved