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
KEYWORD
nonn
AUTHOR
Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 23 2006, Oct 24 2006
STATUS
approved