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Search: id:A093418
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| A093418 |
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Numerator of -3n + 2(1+n)*HarmonicNumber[n]. |
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+0
9
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| 0, 1, 3, 17, 53, 62, 163, 717, 3489, 3727, 43391, 45596, 619313, 644063, 667229, 2756003, 24124223, 24784883, 160941559, 164719333, 33664415, 11451017, 268428987, 819836496, 20845424563, 21181779967, 193553388003
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Average time to quicksort n items in random order.
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REFERENCES
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Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 143 and 258-259, 1996.
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LINKS
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Eric Weisstein's World of Mathematics, Quicksort
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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G.f.: -(x+2*ln(1-x))/(1-x)^2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 05 2004
1+(1/n!)*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*(k-1)*2^k. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 05 2004
a(n) = Numerator[ - n + 2 * H(n, (2)) ], where H(n, (2)) = Sum[HarmonicNumber[k], {k, 1, n}] is second-order harmonic number. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 01 2004
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EXAMPLE
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0, 1, 3, 17/3, 53/6, 62/5, 163/10, 717/35, 3489/140, ... = A093418/A096620
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MATHEMATICA
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Numerator[Table[2*Sum[Sum[1/i, {i, 1, k}], {k, 1, n}]-n, {n, 0, 20}]] or Numerator[Table[2*Sum[HarmonicNumber[k], {k, 1, n}]-n, {n, 0, 20}]]
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CROSSREFS
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Cf. A093412, A093413, A093414, A093415, A093417, A093419, A096620.
Cf. A063090.
Cf. A001008, A002805.
Sequence in context: A132124 A011917 A018691 this_sequence A033562 A130857 A120386
Adjacent sequences: A093415 A093416 A093417 this_sequence A093419 A093420 A093421
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KEYWORD
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nonn,frac
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 30 2004
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EXTENSIONS
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Edited by Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2004
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