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%I #13 Jan 17 2015 23:16:12
%S 1,513,10097891,5170139875,10097934603139727,373997614931101,
%T 15092153145114981831307,7727182467755471289426059,
%U 4106541588424891370931874221019,4106541592523201949266162797531
%N Numerators of sum_{k=1..n} 1/k^9 = Zeta(9,n).
%C a(n) gives the partial sums, Zeta(9,n), of Euler's Zeta(9). 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 A103352 and for the rationals Zeta(9,n) see the W. Lang link under A103345.
%F a(n) = numerator(sum_{k=1..n} 1/k^9).
%F G.f. for rationals Zeta(9, n): polylogarithm(9, x)/(1-x).
%t s=0;lst={};Do[s+=n^1/n^10;AppendTo[lst,Numerator[s]],{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 24 2009 *)
%t Table[ HarmonicNumber[n, 9] // Numerator, {n, 1, 10}] (* _Jean-François Alcover_, Dec 04 2013 *)
%Y For k=1..8 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348, A103349/A103350.
%K nonn,frac,easy
%O 1,2
%A _Wolfdieter Lang_, Feb 15 2005
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