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%I #16 Feb 16 2020 11:54:14
%S 1,5,1313,42169,137969,1128119,8357708899,4784812183,6426498401023,
%T 1290156663524207,2967978587600828623,40788897698984251631,
%U 4438036185262071403841,483740902966638267491,13885929879719429182837579,646524082127557655708798341
%N Numerators of coefficients in a series for the first Stieltjes constant gamma_1.
%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 Th. 1.
%F The reference gives an explicit formula in terms of the Gregory numbers G_n = A002206/A002207.
%t g[n_] := -(-1)^n*Sum[StirlingS1[n, j]/(j + 1), {j, 1, n}]/n!; Table[g[n]/n^2 + Sum[g[k]*g[n + 1 - k]*(HarmonicNumber[n] - HarmonicNumber[k])/(n + 1 - k), {k, 1, n - 1}], {n, 2, 20}] // Numerator (* _Vaclav Kotesovec_, Feb 16 2020 *)
%Y Cf. A002206, A002207, A332537.
%K nonn,frac
%O 2,2
%A _N. J. A. Sloane_, Feb 16 2020
%E More terms from _Vaclav Kotesovec_, Feb 16 2020