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A122720 Number of free generators of degree n of the primitive Lie algebra of the Hopf algebra of parking functions. 0
1, 2, 9, 80, 901, 12564, 206476, 3918025, 84365187, 2034559143, 54368676801, 1595658565373, 51047106371364, 1768603440179357, 65989972332973985, 2638631743605048505, 112577601627965445007, 5105398784598085609386 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

J.-C. Novelli and J.-Y. Thibon, Hopf algebras and dendriform structures arising from parking functions, arXiv:math/0511200 [math.CO], 2005.

FORMULA

G.f.: 1 - Product_{i>=1} (1-t^i)^c(i), where c(i) is the number of connected parking functions of length i.

MATHEMATICA

terms = 18;

s = (1 - 1/(1 + Sum[(n+1)^(n-1)*t^n, {n, 1, terms+1}]))/t + O[t]^(terms+1);

cc = CoefficientList[s, t];

gf = Product[(1 - t^i)^cc[[i]], {i, 1, terms+1}] + O[t]^(terms+1);

CoefficientList[gf, t] // Abs // Rest (* Jean-François Alcover, Feb 17 2019 *)

CROSSREFS

Sequence in context: A194471 A215629 A221460 * A109519 A193208 A279055

Adjacent sequences:  A122717 A122718 A122719 * A122721 A122722 A122723

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 5 03:33 EST 2021. Contains 349530 sequences. (Running on oeis4.)