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Search: id:A103347
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| A103347 |
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Numerators of sum(1/k^7,k=1..n)=:Zeta(7,n). |
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5
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| 1, 129, 282251, 36130315, 2822716691183, 940908897061, 774879868932307123, 99184670126682733619, 650750755630450535274259, 650750820166709327386387, 12681293156341501091194786541177, 12681293507322704937269896541177
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
For the denominators see A103348 and for the rationals Zeta(7,n) see the W. Lang link under A103345.
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FORMULA
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a(n)=numerator(sum(1/k^7, k=1..n)).
G.f. for rationals Zeta(7, n): polylogarithm(7, x)/(1-x).
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MATHEMATICA
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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]
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CROSSREFS
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For k=1..6 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346.
Adjacent sequences: A103344 A103345 A103346 this_sequence A103348 A103349 A103350
Sequence in context: A023876 A143006 A138586 this_sequence A113489 A043604 A025372
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 15 2005
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