1,1

Number of generators of degree n of the Hopf algebra of free quasi-symmetric functions of level 2. For level r, this would be r^n*c(n), where c(n) is the number of connected permutations (A003319).

These are also the dimensions of the graded components of the primitive Lie algebra of the same Hopf algebra.

J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions

2^n*c(n) where c(n) is A003319

a(1)=2 because there are two colourings of the permutation (1).

2^n*op(n, INVERTi([seq(k!, k=1..n)]))

Cf. A003319.

Sequence in context: A012592 A121892 A032107 this_sequence A038049 A038058 A062531

Adjacent sequences: A141304 A141305 A141306 this_sequence A141308 A141309 A141310

nonn

Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008