A141309 INVERTi transform of A141308.

2, 3, 16, 158, 1796, 24250, 372656, 6429927, 122956714, 2581840735, 59084565968, 1464445686726, 39101805324620, 1119446453417490, 34220008384633264, 1112764183812405300, 38362648544330997488, 1397884269388233025156

Offset

1,1

Comments

Number of generators of degree n of the (free) primitive Lie algebra of the Hopf algebra of free quasi-symmetric functions of level 2.

Links

Table of n, a(n) for n=1..18.

J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions, arXiv:0806.3682 [math.CO], 2008.

Maple

INVERTi([seq(d(n, n=1..20)]); # where d(n) is A141308

Mathematica

terms = 18;
c[0] = 0; c[n_] := c[n] = n! - Sum[k! c[n-k], {k, 1, n-1}];
s = (Product[1/(1-x^k)^(2^k c[k]), {k, 1, terms+1}] + O[x]^(terms+1)-1)/x;
CoefficientList[-1/(1 + x s) + O[x]^(terms+1), x] // Rest (* Jean-François Alcover, Feb 13 2019 *)

Crossrefs

Cf. A003319, A141307, A141308.

Sequence in context: A063666 A006247 A052318 * A179442 A299424 A215638

Adjacent sequences: A141306 A141307 A141308 * A141310 A141311 A141312

Keyword

nonn

Author

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

Status

approved