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A122708 Number of connected parking functions of length n. This is the number of independent algebraic generators in degree n of the Hopf algebra of parking functions. 3

%I #19 Jul 10 2017 15:03:50

%S 1,2,11,92,1014,13795,223061,4180785,89191196,2135610879,56749806356,

%T 1658094051392,52851484193553,1825606384989019,67944616806148325,

%U 2710939797419417118,115448074520257458659,5227118335211937247488,250749489074570030593286

%N Number of connected parking functions of length n. This is the number of independent algebraic generators in degree n of the Hopf algebra of parking functions.

%C Dimension of the space of primitive elements of degree n of the Hopf algebra of parking functions.

%H Alois P. Heinz, <a href="/A122708/b122708.txt">Table of n, a(n) for n = 1..300</a>

%H J.-C. Novelli and J.-Y. Thibon, <a href="http://arXiv.org/abs/math.CO/0511200">Hopf algebras and dendriform structures arising from parking functions</a>, arXiv:math/0511200 [math.CO], 2005.

%H 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.

%F G.f.: 1-1/f(t) where f(t) = 1 + sum ( (n+1)^(n-1)*t^n, n >=1).

%F a(n) ~ exp(1) * n^(n-1). - _Vaclav Kotesovec_, Aug 07 2015

%p f:=proc(N);1+sum((n+1)^(n-1)*t^n,n=1..N);end; a:=proc(n);coeff(taylor(1-1/f(n),t,n+1),t,n);end;

%t terms = 19; s = (1-1/(1+Sum[(n+1)^(n-1)*t^n, {n, 1, terms}]))/t + O[t]^terms; CoefficientList[s, t] (* _Jean-Fran├žois Alcover_, Jul 10 2017 *)

%K nonn

%O 1,2

%A Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006, Oct 24 2006

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