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A102928
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Reduced numerators of the harmonic means of the first n positive integers.
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2
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1, 4, 18, 48, 300, 120, 980, 2240, 22680, 25200, 304920, 332640, 4684680, 5045040, 5405400, 11531520, 208288080, 73513440, 1474352880, 62078016, 108636528, 113809696, 2736605872, 8566766208, 223092870000, 232016584800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| See A175441 - denominators of the harmonic means of the first n positive integers. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), May 16 2010]
a(n) is also the denominator of H(n-1)/n + 1/n^2=-int(x^n*ln(1-x),x=0..1) with H(n)= A001008(n)/A002805(n) the harmonic number of order n - From Groux Roland, Jan 08 2011.
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LINKS
| Eric Weisstein's World of Mathematics, Harmonic Mean
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FORMULA
| a(n)=Denominator[EulerGamma/n + PolyGamma[0, 1 + n]/n] [From Artur Jasinski (grafix(AT)csl.pl), Nov 02 2008]
a(n)= Numerator(n/H(n)), where H(n) is the n-th harmonic number. [From Gary Detlefs, Sep 10 2011]
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EXAMPLE
| 1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
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MATHEMATICA
| Table[Denominator[Expand[EulerGamma/a + PolyGamma[0, 1 + a]/a]], {a, 1, 30}] [From Artur Jasinski (grafix(AT)csl.pl), Nov 02 2008]
Table[Numerator[n/HarmonicNumber[n]], {n, 26}]
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CROSSREFS
| Cf. A001008.
Sequence in context: A027271 A073991 A052642 * A081528 A056147 A181857
Adjacent sequences: A102925 A102926 A102927 * A102929 A102930 A102931
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KEYWORD
| nonn,frac
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Jan 19, 2005
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EXTENSIONS
| Roland formula offset corrected by Gary Detlefs, Oct 06 2011
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