cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

1, 1, 9, 3375, 121550625, 3101364196875, 1730690595263722640625, 376292999446907764908950466328125, 16950118160085960270323673755750390625, 90543986887356385297750500755391437150880164126953125
Offset: 0

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Author

Jean-François Alcover, Dec 20 2013

Keywords

Comments

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

Crossrefs

Cf. A164655, A164656, A234144 (numerators).

Programs

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

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.
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