A234145 a(n) = denominator of sum_(k=1..n) 1/(2*k-1)^n.

1, 1, 9, 3375, 121550625, 3101364196875, 1730690595263722640625, 376292999446907764908950466328125, 16950118160085960270323673755750390625, 90543986887356385297750500755391437150880164126953125

Offset

0,3

Comments

The sequence A234144(n)/A234145(n) is Theta(n, n), as defined by Wolfdieter Lang.

Links

Table of n, a(n) for n=0..9.

Wolfdieter Lang, Theta(k, n), k-family of rational sequences and limits.

Formula

a(n) = denominator of (2^n*Zeta(n) - Zeta(n) - Zeta(n, n+1/2))/2^n.

a(n) = denominator of ((-1/2)^n*(PolyGamma(n-1, 1/2) - PolyGamma(n-1, n+1/2)))/(n-1)!.

A234144(n) / A234145(n) ~ 1.

Mathematica

a[n_] := Sum[1/(2*k-1)^n, {k, 1, n}] // Denominator; Table[a[n], {n, 0, 10}]

Crossrefs

Cf. A164655, A164656, A234144 (numerators).

Sequence in context: A281538 A335010 A203744 * A291547 A266458 A238120

Adjacent sequences: A234142 A234143 A234144 * A234146 A234147 A234148

Keyword

nonn,frac,easy

Author

Jean-François Alcover, Dec 20 2013

Status

approved