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%I #13 Sep 08 2022 08:46:10
%S 1,11,15619,2943155,1331492839973,1630880903184421,
%T 31439787218843145032971,1077761962140496544395985052611,
%U 413553884506370765259209008566673121899,88544903809570893686211499586310192741581300347
%N 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.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5 Euler-Mascheroni constant, p. 28.
%D J. J. Mačys, "A new problem," American Mathematical Monthly, (Jan 2012), vol. 119, no. 1, p. 82.
%H G. C. Greubel, <a href="/A249645/b249645.txt">Table of n, a(n) for n = 1..47</a>
%H StackExchange, <a href="http://math.stackexchange.com/questions/605354">Question on Macys formula for Euler-Mascheroni constant gamma</a>, Dec 13 2013.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Euler-MascheroniConstant.html">Euler-Mascheroni Constant</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant">Euler-Mascheroni constant</a>
%e Sequence of fractions begins 1/2, 11/20, 15619/27720, 2943155/5173168, 1331492839973/2329089562800, ...
%t Table[2*HarmonicNumber[n] - HarmonicNumber[n*(n + 1)] // Numerator, {n, 1, 10}]
%o (PARI) {a(n) = 2*sum(k=1,n, 1/k) - sum(k=1,n*(n+1), 1/k)};
%o for(n=1,15, print1(numerator(a(n)), ", ")) \\ _G. C. Greubel_, Sep 04 2018
%o (Magma) [Numerator(2*HarmonicNumber(n) - HarmonicNumber(n*(n + 1))): n in [1..15]]; // _G. C. Greubel_, Sep 04 2018
%Y Cf. A001008, A001620, A002805, A189048, A189049, A249646 (denominators).
%K nonn,frac
%O 1,2
%A _Jean-François Alcover_, Nov 03 2014
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