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Numerators of Sum_{k=1..n} 1/k^7 = Zeta(7,n).
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%I #19 Mar 28 2018 21:59:25

%S 1,129,282251,36130315,2822716691183,940908897061,774879868932307123,

%T 99184670126682733619,650750755630450535274259,

%U 650750820166709327386387,12681293156341501091194786541177,12681293507322704937269896541177

%N Numerators of Sum_{k=1..n} 1/k^7 = Zeta(7,n).

%C a(n) gives the partial sums, Zeta(7,n), of Euler's Zeta(7). 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 A103348 and for the rationals Zeta(7,n) see the W. Lang link under A103345.

%H Robert Israel, <a href="/A103347/b103347.txt">Table of n, a(n) for n = 1..336</a>

%F a(n) = numerator(sum_{k=1..n} 1/k^7).

%F G.f. for rationals Zeta(7, n): polylogarithm(7, x)/(1-x).

%p f:= n -> numer(Psi(6,n+1)/720 + Zeta(7)):

%p map(f, [$1..20]); # _Robert Israel_, Mar 28 2018

%t s=0;lst={};Do[s+=n^1/n^8;AppendTo[lst,Numerator[s]],{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 24 2009 *)

%t Table[ HarmonicNumber[n, 7] // Numerator, {n, 1, 12}] (* _Jean-François Alcover_, Dec 04 2013 *)

%Y For k=1..6 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346.

%K nonn,frac,easy

%O 1,2

%A _Wolfdieter Lang_, Feb 15 2005