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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A234144 a(n) = numerator of Sum_(k=1..n) 1/(2*k - 1)^n.

Original entry on oeis.org

0, 1, 10, 3527, 123296356, 3115356499043, 1733194364791766081374, 376470435881775086250915790503469, 16952748458548438370767527584555153032, 90548635884513844033505877600764150558334149264809109
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, A234145 (denominators).

Programs

  • Maple
    f:= proc(n) local k; numer(add(1/(2*k-1)^n,k=1..n)); end proc:
    map(f, [$0..10]); # Robert Israel, Nov 05 2023
  • Mathematica
    a[n_] := Sum[1/(2*k-1)^n, {k, 1, n}] // Numerator; Table[a[n], {n, 0, 10}]

Formula

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