A164657 Denominators of partial sums of Theta(5) = Sum_{j>=1} 1/(2*j-1)^5.

1, 243, 759375, 12762815625, 3101364196875, 499477805270915625, 185452612752454075153125, 185452612752454075153125, 263316190384861185784690603125, 651996955695764397260286617707209375, 651996955695764397260286617707209375, 4196476041813743307955464949873473110315625

Offset: 1

Author

Wolfdieter Lang, Oct 16 2009

Keywords

• nonn
• frac
• easy

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).

Examples

			Rationals Theta(5,n): [1, 244/243, 762743/759375, 12820180976/12762815625, 3115356499043/3101364196875,...].
		

Programs

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 *)

Formula

a(n) = denominator(Theta(5,n)) = denominator(Sum_{j=1..n} 1/(2*j-1)^5).