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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A232180 First bisection of harmonic numbers (numerators).

Original entry on oeis.org

1, 11, 137, 363, 7129, 83711, 1145993, 1195757, 42142223, 275295799, 18858053, 444316699, 34052522467, 312536252003, 9227046511387, 290774257297357, 53676090078349, 54437269998109, 2040798836801833, 2066035355155033, 85691034670497533
Offset: 1

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Author

Jean-François Alcover and Paul Curtz, Nov 20 2013

Keywords

Comments

Numerator of H(2*n-1), where H(n) = Sum_{k=1..n} 1/k.
It can be noted that the second row of the Akiyama-Tanigawa transform of the fractions A232180/A232181 has a simple expression: -5/6, -9/10, -13/14, -17/18, -21/22, ... are of the form -(4*k+5)/(4*k+6).

Crossrefs

Cf. A001008, A002547, A093158, A175441, A232181 (denominators).

Programs

  • Magma
    [Numerator(HarmonicNumber(2*n-1)): n in [1..30]]; // Bruno Berselli, Nov 20 2013
  • Mathematica
    a[n_] := HarmonicNumber[2*n-1] // Numerator; Table[a[n], {n, 1, 25}]

Formula

a(n) ~ exp(2n).
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