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%I #9 Nov 11 2017 12:08:04
%S 0,0,2,6,44,360,4206,59584,1021432,20329344,461596090,11756157952,
%T 331835099364,10278341179392,346555737301606,12633922368061440,
%U 495139124241620080,20758413862397509632,926980786260912379122,43925328338613823078400,2201264843743619567644700
%N E.g.f.: -tan(x)*LambertW(-x).
%H G. C. Greubel, <a href="/A277479/b277479.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ tan(exp(-1)) * n^(n-1).
%t CoefficientList[Series[-Tan[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
%t Table[Sum[Binomial[n, k] * Sin[Pi*k/2] * 2^(k+1) * (2^(k+1)-1) * BernoulliB[k+1] /(k+1) * (n-k)^(n-k-1), {k, 0, n-1}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o (PARI) x='x+O('x^50); concat([0,0], Vec(serlaplace(- tan(x)*lambertw(-x) ))) \\ _G. C. Greubel_, Nov 08 2017
%Y Cf. A000169, A277467, A277473, A277480.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 17 2016
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