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%I #28 Feb 17 2020 18:14:28
%S 3,1,1,29,67,1507,3121,12703,164551,6344953,147727471,27529188163,
%T 710710333,271695249739,1866529128749,21255957303929,908965802898697,
%U 12844144201070519,228917805573310159,185233029315627847397,104416844507809792139,45256363943072384591371
%N Numerators of coefficients in a series for Euler's constant gamma (negated).
%H Iaroslav V. Blagouchine and Marc-Antoine Coppo, <a href="https://arxiv.org/abs/1703.08601">A note on some constants related to the zeta-function and their relationship with the Gregory coefficients</a>, arXiv:1703.08601 [math.NT], 2017. Also The Ramanujan Journal 47.2 (2018): 457-473. See Cor. 2 to Th. 2.
%H Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">Collection of formulae for Euler's constant gamma</a>.
%F The reference gives an explicit formula in terms of the Gregory numbers G_n = A002206/A002207.
%F gamma = 2*log(2*Pi) - Sum_{k>=0} A332540(k)/A332541(k). - _Hugo Pfoertner_, Feb 16 2020
%t g[n_] := -(-1)^n*Sum[StirlingS1[n, j]/(j + 1), {j, 1, n}]/n!; Flatten[{3, Table[Numerator[2*Sum[g[k]*g[n + 2 - k], {k, 1, n}]/(n + 1)], {n, 1, 25}]}] (* _Vaclav Kotesovec_, Feb 16 2020 *)
%Y Cf. A002206, A002207, A332541.
%Y Cf. A001620 (Euler's constant gamma).
%K nonn,frac
%O 0,1
%A _N. J. A. Sloane_, Feb 16 2020
%E More terms from _Vaclav Kotesovec_, Feb 16 2020
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