A101812 Denominator of the permanent of the n-th Hilbert matrix.

1, 12, 2160, 224000, 470400000, 186313420339200000, 2067909047925770649600000, 365356847125734485878112256000000, 146968826339795671126721851844198400000000

Offset

1,2

Links

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

Formula

Denom(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(denom(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]] // Denominator; 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))); den - Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007

Crossrefs

Cf. A101811.

Sequence in context: A009063 A012675 A175014 * A064074 A005249 A177069

Adjacent sequences: A101809 A101810 A101811 * A101813 A101814 A101815

Keyword

nonn,frac

Author

Emeric Deutsch, Dec 16 2004

Status

approved