A232180 First bisection of harmonic numbers (numerators).

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

Offset

1,2

Comments

Numerator of H(2n+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).

Links

Table of n, a(n) for n=1..21.

Formula

a(n) ~ exp(2n).

Mathematica

a[n_] := HarmonicNumber[2*n-1] // Numerator; Table[a[n], {n, 1, 25}]

Prog

(Magma) [Numerator(HarmonicNumber(2*n-1)): n in [1..30]]; // Bruno Berselli, Nov 20 2013

Crossrefs

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

Sequence in context: A233258 A262382 A142895 * A201111 A124079 A174289

Adjacent sequences: A232177 A232178 A232179 * A232181 A232182 A232183

Keyword

nonn,frac,easy

Author

Jean-François Alcover and Paul Curtz, Nov 20 2013

Status

approved