A101812 - OEIS

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A101812

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

1, 12, 2160, 224000, 470400000, 186313420339200000, 2067909047925770649600000, 365356847125734485878112256000000, 146968826339795671126721851844198400000000 (list; graph; refs; listen; history; internal format)

	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 11/3 + (1/2)(1/2)=7/12.`
	MAPLE	`with(linalg): seq(denom(permanent(hilbert(n))), n=1..12);`
	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=1-2in[j]; in[j]+=z; nc+=z; x+=za[, 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 (deutsch(AT)duke.poly.edu), Dec 16 2004`

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Last modified February 14 09:18 EST 2012. Contains 205614 sequences.