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A164657 Denominators of partial sums of Theta(5) = Sum_{j>=1} 1/(2*j-1)^5. 2
1, 243, 759375, 12762815625, 3101364196875, 499477805270915625, 185452612752454075153125, 185452612752454075153125, 263316190384861185784690603125, 651996955695764397260286617707209375, 651996955695764397260286617707209375, 4196476041813743307955464949873473110315625 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The numerators are given by A164656.
For a reference and a W. Lang link see A164656.
Rationals (partial sums) Theta(5,n) := Sum_{j=1..n} 1/(2*j-1)^5 (in lowest terms). The limit of these rationals is Theta(5)= (1-1/2^5)*Zeta(5) approximately 1.004523763 (Zeta(n) is the Euler-Riemann zeta function).
LINKS
FORMULA
a(n) = denominator(Theta(5,n))= denominator(Sum_{j=1..n} 1/(2*j-1)^5 n>=1.
EXAMPLE
Rationals Theta(5,n): [1, 244/243, 762743/759375, 12820180976/12762815625, 3115356499043/3101364196875,...].
MATHEMATICA
r[n_] := Sum[1/(2*j-1)^5, {j, 1, n}]; (* or r[n_] := (PolyGamma[4, n+1/2] - PolyGamma[4, 1/2])/768 // FullSimplify; *) Table[r[n] // Denominator, {n, 1, 12}] (* Jean-François Alcover, Dec 02 2013 *)
CROSSREFS
Sequence in context: A017309 A017429 A017561 * A151638 A352033 A248137
KEYWORD
nonn,frac,easy,changed
AUTHOR
Wolfdieter Lang, Oct 16 2009
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)