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.

1, 2, 11, 92, 1014, 13795, 223061, 4180785, 89191196, 2135610879, 56749806356, 1658094051392, 52851484193553, 1825606384989019, 67944616806148325, 2710939797419417118, 115448074520257458659, 5227118335211937247488, 250749489074570030593286

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