%I
%S 1,1025,60526249,61978938025,605263128567754849,605263138567754849,
%T 170971856382109814342232401,175075181098169912564190119249,
%U 10338014371627802833957102351534201,413520574906423083987893722912609
%N Numerators of sum(1/k^10,k=1..n)=:Zeta(10,n).
%C 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.
%C For the denominators see A103717 and for the rationals Zeta(10,n) see the W. Lang link under A103345.
%F a(n)=numerator(sum(1/k^10, k=1..n)).
%F G.f. for rationals Zeta(10, n): polylogarithm(10, x)/(1x).
%t 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]
%t Table[ HarmonicNumber[n, 10] // Numerator, {n, 1, 10}] (* _JeanFrançois Alcover_, Dec 04 2013 *)
%Y For k=1..9 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348, A103349/A103350, A103351/A103352.
%K nonn,frac,easy
%O 1,2
%A _Wolfdieter Lang_, Feb 15 2005
