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
KEYWORD
nonn,frac
AUTHOR
Jean-François Alcover, Nov 03 2014
STATUS
approved