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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

%I #17 Feb 17 2019 19:34:25

%S 1,1,2,10,55,377,2892,25007,239286,2514113,28781748,356825354,

%T 4765183277,68227504423,1043012154681,16960950354371,292402844221089,

%U 5327959744239694,102326036191376400,2066148465783001383,43760821265601562218,970152278606623445790

%N 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).

%H G. Duchamp, F. Hivert and J.-Y. Thibon, <a href="https://arxiv.org/abs/math/0105065">Noncommutative symmetric functions VI: Free quasi-symmetric functions and related algebras</a>, arXiv:math/0105065 [math.CO], 2001; Internat. J. Alg. Comp. 12 (2002), 671-717

%H L. Foissy, <a href="https://arxiv.org/abs/math/0505207">Bidendriform bialgebras, trees and free quasi-symmetric functions</a>, arXiv:math/0505207 [math.RA], 2005.

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

%t terms = 22;

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

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

%t CoefficientList[gf, t] // Rest (* _Jean-François Alcover_, Feb 17 2019 *)

%Y Cf. A003319.

%K nonn

%O 1,3

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

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)