A103351 Numerators of sum_{k=1..n} 1/k^9 = Zeta(9,n).

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.

Links

Table of n, a(n) for n=1..10.

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 *)

Crossrefs

For k=1..8 see: A001008/A002805, A007406/A007407, A007408/A007409, A007410/A007480, A099828/A069052, A103345/A103346, A103347/A103348, A103349/A103350.

Sequence in context: A118709 A296145 A283369 * A291507 A275099 A238615

Adjacent sequences: A103348 A103349 A103350 * A103352 A103353 A103354

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Feb 15 2005

Status

approved