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A103716 Numerators of sum_{k=1..n} 1/k^10 =: Zeta(10,n). 2


%S 1,1025,60526249,61978938025,605263128567754849,605263138567754849,

%T 170971856382109814342232401,175075181098169912564190119249,

%U 10338014371627802833957102351534201,413520574906423083987893722912609

%N Numerators of sum_{k=1..n} 1/k^10 =: 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_{k=1..n} 1/k^10).

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

%t s=0;lst={};Do[s+=n^1/n^11;AppendTo[lst,Numerator[s]],{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 24 2009 *)

%t Table[ HarmonicNumber[n, 10] // Numerator, {n, 1, 10}] (* _Jean-Fran├žois 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

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