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A249645 Numerators 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
1, 11, 15619, 2943155, 1331492839973, 1630880903184421, 31439787218843145032971, 1077761962140496544395985052611, 413553884506370765259209008566673121899, 88544903809570893686211499586310192741581300347 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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)] // Numerator, {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(numerator(a(n)), ", ")) \\ G. C. Greubel, Sep 04 2018

(MAGMA) [Numerator(2*HarmonicNumber(n) - HarmonicNumber(n*(n + 1))): n in [1..15]]; // G. C. Greubel, Sep 04 2018

CROSSREFS

Cf. A001008, A001620, A002805, A189048, A189049, A249646 (denominators).

Sequence in context: A061965 A013748 A076783 * A145526 A230220 A068647

Adjacent sequences:  A249642 A249643 A249644 * A249646 A249647 A249648

KEYWORD

nonn,frac

AUTHOR

Jean-François Alcover, Nov 03 2014

STATUS

approved

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Last modified June 27 07:19 EDT 2022. Contains 354889 sequences. (Running on oeis4.)