A249646 Denominators of 2*H(n)-H(n*(n+1)), a sequence the limit of which is gamma, the Euler-Mascheroni constant, where H(n) is the n-th harmonic number.

2, 20, 27720, 5173168, 2329089562800, 2844937529085600, 54749786241679275146400, 1874681189225708508850515710400, 718766754945489455304472257065075294400, 153803387341307877636928566091115101174034840640

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5 Euler-Mascheroni constant, p. 28.

J. J. Mačys, "A new problem," American Mathematical Monthly, (Jan 2012), vol. 119, no. 1, p. 82.

Links

G. C. Greubel, Table of n, a(n) for n = 1..47

StackExchange, Question on Macys formula for Euler-Mascheroni constant gamma, Dec 13 2013.

Eric Weisstein's MathWorld, Euler-Mascheroni Constant

Wikipedia, Euler-Mascheroni constant

Example

Sequence of fractions begins 1/2, 11/20, 15619/27720, 2943155/5173168, 1331492839973/2329089562800, ...

Mathematica

Table[2*HarmonicNumber[n] - HarmonicNumber[n*(n + 1)] // Denominator, {n, 1, 10}]

Prog

(PARI) {a(n) = 2*sum(k=1, n, 1/k) - sum(k=1, n*(n+1), 1/k)};
for(n=1, 15, print1(denominator(a(n)), ", ")) \\ G. C. Greubel, Sep 04 2018
(Magma) [Denominator(2*HarmonicNumber(n) - HarmonicNumber(n*(n + 1))): n in [1..15]]; // G. C. Greubel, Sep 04 2018

Crossrefs

Cf. A001008, A001620, A002805, A189048, A189049, A249645 (numerators).

Sequence in context: A060600 A356689 A346564 * A143247 A342079 A303216

Adjacent sequences: A249643 A249644 A249645 * A249647 A249648 A249649

Keyword

nonn,frac

Author

Jean-François Alcover, Nov 03 2014

Status

approved