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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
 1, 2, 11, 92, 1014, 13795, 223061, 4180785, 89191196, 2135610879, 56749806356, 1658094051392, 52851484193553, 1825606384989019, 67944616806148325, 2710939797419417118, 115448074520257458659, 5227118335211937247488, 250749489074570030593286 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Dimension of the space of primitive elements of degree n of the Hopf algebra of parking functions. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..300 J.-C. Novelli and J.-Y. Thibon, Hopf algebras and dendriform structures arising from parking functions, arXiv:math/0511200 [math.CO], 2005. Jean-Christophe Novelli and Jean-Yves Thibon, Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions (2008); arXiv:0806.3682 [math.CO]. Discrete Math. 310 (2010), no. 24, 3584-3606. FORMULA G.f.: 1-1/f(t) where f(t) = 1 + sum ( (n+1)^(n-1)*t^n, n >=1). a(n) ~ exp(1) * n^(n-1). - Vaclav Kotesovec, Aug 07 2015 MAPLE 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; MATHEMATICA 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 *) CROSSREFS Sequence in context: A047854 A366402 A222080 * A337012 A322767 A292424 Adjacent sequences: A122705 A122706 A122707 * A122709 A122710 A122711 KEYWORD nonn AUTHOR Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006, Oct 24 2006 STATUS approved

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Last modified December 4 18:21 EST 2023. Contains 367563 sequences. (Running on oeis4.)