The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A350669 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A350669

Numerators of Sum_{j=0..n} 1/(2*j+1), for n >= 0.
(history; published version)

#27 by Michael De Vlieger at Sun Aug 13 17:33:16 EDT 2023

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proposed

approved

#26 by Michel Marcus at Sun Aug 13 15:59:14 EDT 2023

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editing

proposed

#25 by Michel Marcus at Sun Aug 13 15:59:11 EDT 2023

LINKS

Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=150&Page=258"> Handbook of Mathematical Functions. p.258</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. p. 258.

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approved

editing

#24 by Alois P. Heinz at Mon Jul 24 10:54:17 EDT 2023

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proposed

approved

#23 by Robert C. Lyons at Mon Jul 24 10:46:57 EDT 2023

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editing

proposed

#22 by Robert C. Lyons at Mon Jul 24 10:46:48 EDT 2023

FORMULA

a(n) = (1/2) * numerator of ( 2*H_{2*n+2} - H_{n+1} ), where H_{n} is the nth n-th Harmonic number. - G. C. Greubel, Jul 24 2023

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approved

editing

#21 by Joerg Arndt at Mon Jul 24 04:23:07 EDT 2023

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reviewed

approved

#20 by Michel Marcus at Mon Jul 24 03:54:01 EDT 2023

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proposed

reviewed

#19 by G. C. Greubel at Mon Jul 24 03:04:13 EDT 2023

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editing

proposed

#18 by G. C. Greubel at Mon Jul 24 03:04:04 EDT 2023

FORMULA

a(n) = (1/2) * numerator of ( 2*H_{2*n+2} - H_{n+1} ), where H_{n} is the nth Harmonic number. - G. C. Greubel, Jul 24 2023

MATHEMATICA

With[{H=HarmonicNumber}, Table[Numerator[2*H[2*n+2] -H[n+1]]/2 , {n, 0, 50}]] (* G. C. Greubel, Jul 24 2023 *)

PROG

(Magma) [Numerator((2*HarmonicNumber(2*n+2) - HarmonicNumber(n+1)))/2: n in [0..40]]; // G. C. Greubel, Jul 24 2023

(SageMath) [numerator(2*harmonic_number(2*n+2, 1) - harmonic_number(n+1, 1))/2 for n in range(41)] # G. C. Greubel, Jul 24 2023

CROSSREFS

Cf. A001620, A025547, A025550, A111877 (denominators), A350670.

STATUS

approved

editing