|
| |
|
|
A102928
|
|
Reduced numerators of the harmonic means of the first n positive integers.
|
|
3
|
|
|
|
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;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
See A175441 - denominators of the harmonic means of the first n positive integers. [From Jaroslav Krizek, 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.
|
|
|
LINKS
|
Table of n, a(n) for n=1..26.
Eric Weisstein's World of Mathematics, Harmonic Mean
|
|
|
FORMULA
|
a(n) = denominator(EulerGamma/n + PolyGamma(0, 1 + n)/n). [Artur Jasinski, Nov 02 2008]
a(n) = numerator(n/H(n)), where H(n) is the n-th harmonic number. [Gary Detlefs, Sep 10 2011]
a(n) = denominator(sum(1/(k*(k+n)), k=1..oo)). [Paolo P. Lava, Jan 17 2013]
|
|
|
EXAMPLE
|
1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363, 2240/761, ...
|
|
|
MATHEMATICA
|
Table[Denominator[Expand[EulerGamma/a + PolyGamma[0, 1 + a]/a]], {a, 1, 30}] [Artur Jasinski, Nov 02 2008]
Table[Numerator[n/HarmonicNumber[n]], {n, 26}]
|
|
|
CROSSREFS
|
Cf. A001008.
Sequence in context: A027271 A073991 A052642 * A081528 A056147 A181857
Adjacent sequences: A102925 A102926 A102927 * A102929 A102930 A102931
|
|
|
KEYWORD
|
nonn,frac
|
|
|
AUTHOR
|
Eric W. Weisstein, Jan 19, 2005
|
|
|
EXTENSIONS
|
Roland formula offset corrected by Gary Detlefs, Oct 06 2011
|
|
|
STATUS
|
approved
|
| |
|
|
