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Search: id:A103351
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| A103351 |
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Numerators of sum(1/k^9,k=1..n)=:Zeta(9,n). |
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3
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| 1, 513, 10097891, 5170139875, 10097934603139727, 373997614931101, 15092153145114981831307, 7727182467755471289426059, 4106541588424891370931874221019, 4106541592523201949266162797531
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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(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.
For the denominators see A103352, and for the rationals Zeta(9,n) see the W. Lang link under A103345.
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FORMULA
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a(n)=numerator(sum(1/k^9, k=1..n)).
G.f. for rationals Zeta(9, n): polylogarithm(9, x)/(1-x).
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CROSSREFS
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For k=1..8 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348, A103349/A103350.
Sequence in context: A086030 A094647 A118709 this_sequence A045054 A116013 A043380
Adjacent sequences: A103348 A103349 A103350 this_sequence A103352 A103353 A103354
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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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