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%I #5 Dec 18 2019 09:02:30
%S 1,1,2,10,48,344,2400,22128,223104,2520576,30689280,415560960,
%T 6058229760,95710187520,1602520657920,28908021381120,554882885222400,
%U 11182172398387200,237581975468113920,5324332409912033280,125630406117045043200
%N Expansion of e.g.f. Product_{k>=1} (1 + arctan(x^k)).
%F E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arctan(x^(k/d))^d / d).
%t nmax = 20; CoefficientList[Series[Product[(1 + ArcTan[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) ArcTan[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A010050, A270666, A330544.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 17 2019