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A122827 Number of independent generators of degree n of the algebra of Free quasi-symmetric functions (or Malvenuto-Reutenauer algebra of permutations) as a dendriform dialgebra (i.e., number of totally primitive elements). 1
1, 0, 1, 6, 39, 284, 2305, 20682, 203651, 2186744, 25463925, 319989030, 4320183527, 62412737460, 961264517369, 15730347890082, 272650924761195, 4991218317261808, 96248879172426557, 1950405560049871134, 41440841509597888495, 921333064567137032620, 21392807067461981820417 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..23.

G. Duchamp, F. Hivert and J.-Y. Thibon, Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras, arXiv:math/0105065 [math.CO], 2001; Internat. J. Alg. Comp. 12 (2002), 671-717

L. Foissy, Bidendriform bialgebras, trees and free quasi-symmetric functions, arXiv:math/0505207 [math.RA], 2005.

Foissy, L.  Plane posets, special posets, and permutations,  Adv. Math. 240, 24-60 (2013).

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.: (f(t)-1)/f(t)^2, where f(t)=sum(n!*t^n,n>=0)

a(n) ~ n! * (1 - 4/n + 1/n^2 - 3/n^3 - 34/n^4 - 313/n^5 - 3189/n^6 - 36670/n^7 - 471381/n^8 - 6700559/n^9 - 104359132/n^10 - ...). - Vaclav Kotesovec, Feb 13 2019

MATHEMATICA

terms = 23; f[t_] = 1 + Sum[n! t^n, {n, 1, terms+1}];

CoefficientList[(f[t]-1)/f[t]^2 + O[t]^(terms+1), t] // Rest (* Jean-Fran├žois Alcover, Feb 13 2019 *)

CROSSREFS

Sequence in context: A153392 A253077 A231482 * A103194 A009018 A289996

Adjacent sequences:  A122824 A122825 A122826 * A122828 A122829 A122830

KEYWORD

nonn

AUTHOR

Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 23 2006

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)