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terms = 19; s = (1-1/(1+Sum[(n+1)^(n-1)*t^n, {n, 1, terms}]))/t + O[t]^terms; CoefficientList[s, t] (* Jean-François Alcover, Jul 10 2017 *)
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Jean-Christophe Novelli and Jean-Yves Thibon, <a href="http://arxiv.org/abs/0806.3682">Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions</a> (2008); arXiv:0806.3682 [math.CO]. Discrete Math. 310 (2010), no. 24, 3584-3606.
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J.-C. Novelli and J.-Y. Thibon, <a href="http://fr.arXiv.org/abs/math.CO/0511200">Hopf algebras and dendriform structures arising from parking functions</a>, arXiv:math/0511200 [math.CO], 2005.
Generating functionG.f.: sum a(n)*t^n = 1-1/f(t) where f(t) = 1 + sum ( (n+1)^(n-1)*t^n, n >=1).
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a(n) ~ exp(1) * n^(n-1). - Vaclav Kotesovec, Aug 07 2015
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