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A122826 Number of free generators of degree n of the primitive Lie algebra of the Hopf algebra of Free quasi-symmetric functions (or Malvenuto-Reutenauer algebra of permutations). 0
1, 1, 2, 10, 55, 377, 2892, 25007, 239286, 2514113, 28781748, 356825354, 4765183277, 68227504423, 1043012154681, 16960950354371, 292402844221089, 5327959744239694, 102326036191376400, 2066148465783001383, 43760821265601562218, 970152278606623445790 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..22.

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.

FORMULA

G.f.: 1 - Product_{n>=1} (1-t^n)^A003319(n).

MATHEMATICA

terms = 22;

(* b = A003319 *) b[0]=0; b[n_] := b[n] = n! - Sum[k!*b[n-k], {k, 1, n-1}];

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

CoefficientList[gf, t] // Rest (* Jean-Fran├žois Alcover, Feb 17 2019 *)

CROSSREFS

Cf. A003319.

Sequence in context: A268556 A175935 A216721 * A320129 A329871 A108490

Adjacent sequences:  A122823 A122824 A122825 * A122827 A122828 A122829

KEYWORD

nonn

AUTHOR

Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 23 2006, Oct 24 2006

STATUS

approved

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Last modified June 24 12:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)