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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
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-François Alcover, Feb 17 2019 *)
CROSSREFS
Cf. A003319.
Sequence in context: A371816 A175935 A216721 * A320129 A329871 A108490
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 April 23 01:19 EDT 2024. Contains 371906 sequences. (Running on oeis4.)