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A103351
Numerators of sum_{k=1..n} 1/k^9 = Zeta(9,n).
3
1, 513, 10097891, 5170139875, 10097934603139727, 373997614931101, 15092153145114981831307, 7727182467755471289426059, 4106541588424891370931874221019, 4106541592523201949266162797531
OFFSET
1,2
COMMENTS
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.
FORMULA
a(n) = numerator(sum_{k=1..n} 1/k^9).
G.f. for rationals Zeta(9, n): polylogarithm(9, x)/(1-x).
MATHEMATICA
s=0; lst={}; Do[s+=n^1/n^10; AppendTo[lst, Numerator[s]], {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 24 2009 *)
Table[ HarmonicNumber[n, 9] // Numerator, {n, 1, 10}] (* Jean-François Alcover, Dec 04 2013 *)
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Feb 15 2005
STATUS
approved