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%I #18 Feb 16 2020 12:13:15
%S 3,1,1,7,1,43,79,717,3481,100189,533077,1777722593,156155179,
%T 74216302403,15537618841,11069240202341,5762870563187,
%U 2682308717818019,927089189292457,3726882116303677517,35762248102620751,1529769611935770520751,1576432862602739502061
%N Numerators of coefficients in a series for log(2 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 Cor. 1 to Th. 2.
%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[{3, Numerator[Table[Sum[g[k]*g[n + 1 - k], {k, 1, n}]/n, {n, 1, 30}]]}] (* _Vaclav Kotesovec_, Feb 16 2020 *)
%Y Cf. A002206, A002207, A332539.
%Y Cf. A061444 (log(2*Pi)).
%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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