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A332539 Denominators of coefficients in a series for log(2 Pi).

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%I A332539 #17 Feb 16 2020 12:13:49
%S A332539 2,4,24,432,120,8640,24192,313600,2073600,78382080,532224000,
%T A332539 2212987392000,237758976000,135998134272000,33798352896000,
%U A332539 28245766348800000,17072996548608000,9142589651779584000,3606419447414784000,16427702944441958400000,177473799122780160000
%N A332539 Denominators of coefficients in a series for log(2 Pi).
%H A332539 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. 1 to Th. 2.
%F A332539 The reference gives an explicit formula in terms of the Gregory numbers G_n = A002206/A002207.
%t A332539 g[n_] := -(-1)^n*Sum[StirlingS1[n, j]/(j + 1), {j, 1, n}]/n!; Flatten[{2, Denominator[Table[Sum[g[k]*g[n + 1 - k], {k, 1, n}]/n, {n, 1, 30}]]}] (* _Vaclav Kotesovec_, Feb 16 2020 *)
%Y A332539 Cf. A002206, A002207, A332538.
%Y A332539 Cf. A061444 (log(2*Pi)).
%K A332539 nonn,frac
%O A332539 0,1
%A A332539 _N. J. A. Sloane_, Feb 16 2020
%E A332539 More terms from _Vaclav Kotesovec_, Feb 16 2020