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%I #14 Feb 16 2020 11:54:37
%S 2,6,32,432,207360,10368000,48384000,533433600,5120962560000,
%T 3687093043200,6083703521280000,1472256252149760000,
%U 4019259568368844800000,64690939719460454400000,8151058404652017254400000,1018882300581502156800000,33256318290980230397952000000
%N Denominators of coefficients in a series for the first Stieltjes constant gamma_1.
%C Note the offset here is different from that in A332536 (because A332536(1) would be Pi).
%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!; Flatten[{2, 6, Denominator[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}]]}] (* _Vaclav Kotesovec_, Feb 16 2020 *)
%Y Cf. A002206, A002207, A332536.
%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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