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%I #9 May 30 2018 03:57:17
%S 0,1,2,14,116,1376,19926,346128,6964712,159396352,4085415850,
%T 115906440704,3605365584732,121998144397312,4461190462108030,
%U 175305587376883712,7366747721719011280,329646098258032459776,15649117182518598570834,785528920149992297070592
%N E.g.f.: tan(x)/(1+LambertW(-x)).
%H G. C. Greubel, <a href="/A277467/b277467.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ tan(exp(-1)) * n^n.
%t CoefficientList[Series[Tan[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
%t Table[Sin[Pi*n/2] * 2^(n+1) * (2^(n+1) - 1) * BernoulliB[n+1] / (n+1) + Sum[Binomial[n, k] * Sin[Pi*k/2] * 2^(k+1) * (2^(k+1)-1) * BernoulliB[k+1] /(k+1) * (n-k)^(n-k), {k, 0, n-1}], {n, 0, 25}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(tan(x)/(1 + lambertw(-x))))) \\ _G. C. Greubel_, May 29 2018
%Y Cf. A000312, A086331, A277468.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 16 2016
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