%I #10 Feb 17 2019 19:34:18
%S 1,2,9,80,901,12564,206476,3918025,84365187,2034559143,54368676801,
%T 1595658565373,51047106371364,1768603440179357,65989972332973985,
%U 2638631743605048505,112577601627965445007,5105398784598085609386
%N Number of free generators of degree n of the primitive Lie algebra of the Hopf algebra of parking functions.
%H J.-C. Novelli and J.-Y. Thibon, <a href="https://arxiv.org/abs/math/0511200">Hopf algebras and dendriform structures arising from parking functions</a>, arXiv:math/0511200 [math.CO], 2005.
%F G.f.: 1 - Product_{i>=1} (1-t^i)^c(i), where c(i) is the number of connected parking functions of length i.
%t terms = 18;
%t s = (1 - 1/(1 + Sum[(n+1)^(n-1)*t^n, {n, 1, terms+1}]))/t + O[t]^(terms+1);
%t cc = CoefficientList[s, t];
%t gf = Product[(1 - t^i)^cc[[i]], {i, 1, terms+1}] + O[t]^(terms+1);
%t CoefficientList[gf, t] // Abs // Rest (* _Jean-François Alcover_, Feb 17 2019 *)
%K nonn
%O 1,2
%A Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006, Oct 24 2006