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%I #7 Nov 13 2017 02:45:54
%S 0,1,2,7,48,469,5584,80235,1367040,26840841,595623680,14752565807,
%T 403579762688,12084385256605,393093330282496,13804177426246995,
%U 520496287836012544,20973496057176404881,899452315670554017792,40903215737685386469847
%N E.g.f.: -LambertW(-arctan(x)).
%H G. C. Greubel, <a href="/A277503/b277503.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ sqrt(sin(2*exp(-1))/2) * exp(-n + 1/2) * n^(n-1) / tan(exp(-1))^n.
%t CoefficientList[Series[-LambertW[-ArcTan[x]], {x, 0, 20}], x] * Range[0, 20]!
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-atan(x))))) \\ _G. C. Greubel_, Nov 12 2017
%Y Cf. A277502.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 18 2016
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