%I A103347
%S A103347 1,129,282251,36130315,2822716691183,940908897061,774879868932307123,
%T A103347 99184670126682733619,650750755630450535274259,650750820166709327386387,
%U A103347 12681293156341501091194786541177,12681293507322704937269896541177
%N A103347 Numerators of sum(1/k^7,k=1..n)=:Zeta(7,n).
%C A103347 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 A103347 For the denominators see A103348 and for the rationals Zeta(7,n) see 
               the W. Lang link under A103345.
%F A103347 a(n)=numerator(sum(1/k^7, k=1..n)).
%F A103347 G.f. for rationals Zeta(7, n): polylogarithm(7, x)/(1-x).
%t A103347 s=0;lst={};Do[s+=n^1/n^8;AppendTo[lst,Numerator[s]],{n,3*4!}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 24 2009]
%Y A103347 For k=1..6 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/
               A007480, A099828/A069052, A103345/A103346.
%Y A103347 Sequence in context: A023876 A143006 A138586 this_sequence A113489 A043604 
               A025372
%Y A103347 Adjacent sequences: A103344 A103345 A103346 this_sequence A103348 A103349 
               A103350
%K A103347 nonn,frac,easy
%O A103347 1,2
%A A103347 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Feb 15 2005