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Search: id:A103716
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| A103716 |
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Numerators of sum(1/k^10,k=1..n)=:Zeta(10,n). |
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+0
2
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| 1, 1025, 60526249, 61978938025, 605263128567754849, 605263138567754849, 170971856382109814342232401, 175075181098169912564190119249, 10338014371627802833957102351534201, 413520574906423083987893722912609
(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(10,n) of Euler's Zeta(10). 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 A103717 and for the rationals Zeta(10,n) see the W. Lang link under A103345.
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FORMULA
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a(n)=numerator(sum(1/k^10, k=1..n)).
G.f. for rationals Zeta(10, n): polylogarithm(10, x)/(1-x).
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MATHEMATICA
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s=0; lst={}; Do[s+=n^1/n^11; 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..9 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348, A103349/A103350, A103351/A103352.
Sequence in context: A013958 A036088 A023002 this_sequence A031530 A004607 A066133
Adjacent sequences: A103713 A103714 A103715 this_sequence A103717 A103718 A103719
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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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