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A103349
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Numerators of sum(1/k^8,k=1..n)=:Zeta(8,n).
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3
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1, 257, 1686433, 431733409, 168646292872321, 168646392872321, 972213062238348973121, 248886558707571775009601, 1632944749460578249437992161, 1632944765723715465050248417
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) gives the partial sums, Zeta(8,n) of Euler's Zeta(8). 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 A103350 and for the rationals Zeta(8,n) see the W. Lang link under A103345.
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FORMULA
| a(n)=numerator(sum(1/k^8, k=1..n)).
G.f. for rationals Zeta(8, n): polylogarithm(8, x)/(1-x).
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MATHEMATICA
| s=0; lst={}; Do[s+=n^1/n^9; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 24 2009]
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CROSSREFS
| For k=1..7 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348.
Sequence in context: A086022 A125649 A097736 * A194155 A121237 A161683
Adjacent sequences: A103346 A103347 A103348 * A103350 A103351 A103352
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KEYWORD
| nonn,frac,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 15 2005
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