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%I #6 Dec 17 2019 19:11:12
%S 1,1,4,16,104,704,6368,58752,662272,7802880,106639872,1511241216,
%T 24062834688,398765162496,7252942872576,137324083666944,
%U 2804224273514496,59594575901687808,1352293406316822528,31831016595468189696
%N Expansion of e.g.f. Product_{k>=1} 1 / (1 - arctan(x^k)).
%F E.g.f.: exp(Sum_{k>=1} Sum_{d|k} arctan(x^(k/d))^d / d).
%t nmax = 19; CoefficientList[Series[Product[1/(1 - ArcTan[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 19; CoefficientList[Series[Exp[Sum[Sum[ArcTan[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A010050, A270665, A330538.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 17 2019