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A103716 Numerators of sum(1/k^10,k=1..n)=:Zeta(10,n). 1
1, 1025, 60526249, 61978938025, 605263128567754849, 605263138567754849, 170971856382109814342232401, 175075181098169912564190119249, 10338014371627802833957102351534201, 413520574906423083987893722912609 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) gives the partial sums, Zeta(10,n) of Euler's Zeta(10). Zeta(k,n) is also called H(k,n) because for k=1 these are the harmonic numbers H(n) = A001008/A002805.

For the denominators see A103717 and for the rationals Zeta(10,n) see the W. Lang link under A103345.

LINKS

Table of n, a(n) for n=1..10.

FORMULA

a(n)=numerator(sum(1/k^10, k=1..n)).

G.f. for rationals Zeta(10, n): polylogarithm(10, x)/(1-x).

MATHEMATICA

s=0; lst={}; Do[s+=n^1/n^11; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst [From Vladimir Joseph Stephan Orlovsky, Jan 24 2009]

Table[ HarmonicNumber[n, 10] // Numerator, {n, 1, 10}] (* Jean-Fran├žois Alcover, Dec 04 2013 *)

CROSSREFS

For k=1..9 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348, A103349/A103350, A103351/A103352.

Sequence in context: A023002 A168119 A180270 * A031530 A004607 A221008

Adjacent sequences:  A103713 A103714 A103715 * A103717 A103718 A103719

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang, Feb 15 2005

STATUS

approved

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Last modified July 31 23:45 EDT 2014. Contains 245090 sequences.