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A096620 Denominator of -3n + 2(1+n)*HarmonicNumber(n). 6
1, 1, 1, 3, 6, 5, 10, 35, 140, 126, 1260, 1155, 13860, 12870, 12012, 45045, 360360, 340340, 2042040, 1939938, 369512, 117572, 2586584, 7436429, 178474296, 171609900, 1487285800, 1434168450, 40156716600, 38818159380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also, with initial term 0 (really this is A093419), denominator of q_n = -4n + 2(1+n)*HarmonicNumber[n] (Cameron). Cf. A115107.

Average time to quicksort n items in random order.

REFERENCES

P. J. Cameron, Combinatorics, Cambridge Univ. Press, 1996, see p. 68.

M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 4.

LINKS

Table of n, a(n) for n=0..29.

Eric Weisstein's World of Mathematics, Quicksort

FORMULA

a(n) = Denominator(2*(n+1)*HarmonicNumber(n+1)-1). - Gary Detlefs, Sep 14 2011

a(n) = Denominator((H(n+1) + H(n))/(H(n+1) - H(n))), where H(n) is the n-th harmonic number. - Gary Detlefs, Oct 03 2011

EXAMPLE

0, 1, 3, 17/3, 53/6, 62/5, 163/10, 717/35, 3489/140, ...

CROSSREFS

Cf. A093418, A115107.

Sequence in context: A246978 A127780 A118413 * A093419 A160049 A007479

Adjacent sequences:  A096617 A096618 A096619 * A096621 A096622 A096623

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Jul 01 2004

EXTENSIONS

Offset corrected by Gary Detlefs, Sep 14 2011

STATUS

approved

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Last modified March 28 21:25 EDT 2017. Contains 284246 sequences.