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%I #6 May 11 2022 10:37:34
%S 1,-2,-2,-16,-16,16,-832,-22016,-27648,173568,-4228608,-57965568,
%T -398991360,2554896384,-98606039040,-7568860053504,-17762113880064,
%U 200091412463616,-7331825098948608,-258326401420099584,-2009778629489197056,25949098553870647296,-1278044473427380666368
%N Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + arctan(x).
%t nn = 23; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - ArcTan[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y Cf. A010050, A353820, A353911, A353913, A353914.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, May 10 2022
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