A093158 -id:A093158 - cp's OEIS frontend

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

Jean-François Alcover and Paul Curtz, Nov 20 2013

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).

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

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

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

a(n) ~ exp(2n).

A093159 Reduced denominators of the raw moments of the distribution of areas for triangles picked at random in a unit square.

Original entry on oeis.org

1, 144, 96, 72000, 2400, 3512320, 27095040, 870912000, 24192000, 103038566400, 1873428480, 12223042191360, 35258775552000, 99189522432000, 1889324236800, 25062074933575680, 61426654248960, 1101504369917952000

Offset: 1

Eric W. Weisstein, Mar 26 2004; Jan 27 2005

			1, 11/144, 1/96, 137/72000, 1/2400, 363/3512320, ...

Eric Weisstein's World of Mathematics, Square Triangle Picking

Cf. A093158.

(3*2^(3 - n)*(1 + (2 + n)*HarmonicNumber[1 + n]))/((1 + n)*(2 + n)^3*(3 + n)^2).

cp's OEIS Frontend

A232180 First bisection of harmonic numbers (numerators).

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